1 Introduction

This is the notebook associated with the publication “TITLE”. The code required to replicate the results can be found below. An additional accompanying file is also made avaiable in the same github directory containing the various functions used in this study. In a nutshell, participants unerwent 2 weeks of EMA, coupled with EPA (physiological arousal measures acquired via a wearable). One week has a high stakes exam, while the other is a control week. We look at the differences between the weeks, and then try to see momentary associations, followed by the ability of ML Models to classify the week types. Data can be made avaialbe upon request. Before we begin though, we load in all the libraries used. All libraries used must first be loaded. It may be that some libraries are not used, and that is due to edits and rewrites, but we keep them loaded just in case.

In addition to loading librarires, we also make a preset theme for the graphs to plot editing a bit easier. For that reason, we specify themes here. Additionally, we specify the number of cores we need, as this is important in perfroming some parallel analysis.

# Theme 1
ggtheme <- theme (text=element_text(size=16,  family="Cambria"),
                  legend.position = "none",
                  axis.text.y = element_blank(),axis.text.x = element_text(size=16),
                  axis.ticks.y = element_blank(),
                  plot.title = element_text(size=16, hjust=0.5),
                  panel.background = element_rect(fill="transparent"),
                  panel.grid.minor.y = element_line(size=3),
                  panel.grid.major = element_line(colour = "aliceblue") )
# Theme 2
ptheme <- theme(text=element_text(size=11,  family="Calibri"), 
          axis.line = element_line(size = 1, colour = "grey"),
          panel.background = element_rect(fill="transparent"),
    plot.background = element_rect(fill = "transparent", color = NA), # bg of the plot
        panel.grid.minor.y = element_line(colour="grey95"),
        panel.grid.major.y = element_line(colour = "grey95")) 
  
# Set number of cores
NoCores <- as.numeric(availableCores())-1
  

Some custom functions were used as part of this study, and must be loaded. These functions are also provided in this github directory.

source("functions.R")

2 Data

Now that all the set-up has been complete, we can start with loading the data. Due to privacy issues, only a specific file (and not the full file) with anonymized categorical variables for the program are provided in this code. This contains the same data used in the analysis, but with recoding of factors to mask potential identifiers. This has also been cleaned to generate a few different variables required for analysis using functions in the “function.R” file. These variables are given a specific suffix as described below:

  • _c: Variable is subject mean centered
  • _z: Variable is z-transformed at the population level (centered and scaled)
  • _s: Variable is Z-transformed and rescaled to 1-10 for analysis with different model families
  • _m: Variable mean in each week for each subject
  • _mz: Variable mean from above is z-transformed
  • _l: Variable is Temporally Lagged (-1)
  • _cs: Variable is subject centered, then rescaled to 1-10
#read.csv("data/EMA_Clean_Anon.csv")
print(EMA_Pub)
Warning messages:
1: Unknown or uninitialised column: `completed`. 
2: Unknown or uninitialised column: `completed`. 
3: Unknown or uninitialised column: `completed`. 
4: Unknown or uninitialised column: `completed`. 
5: Unknown or uninitialised column: `completed`. 
6: Unknown or uninitialised column: `completed`. 
7: Unknown or uninitialised column: `completed`. 
8: Unknown or uninitialised column: `completed`. 
9: Unknown or uninitialised column: `completed`. 

2.1 Mean Stress

For some basic analysis, we also get the mean of the subjective stress measures. These are used for visualization.

##Average stress Measure
EMA_Data$mean_stress <- rowSums(EMA_Data[c('event_tot_z', 'activity_tot_z', 'social_tot_z')], na.rm=TRUE)
EMA_Data$mean_stress_c <- rowSums(EMA_Data[c('event_tot_c', 'activity_tot_c', 'social_tot_c')], na.rm=TRUE)
EMA_Data$mean_stress_s <- scales::rescale(EMA_Data$mean_stress_c, to=c(1, 10))
EMA_Data$mean_stress_l <- lag_var(x="mean_stress_c", id="Sub_nr_week", obs="obs", day= "ema_day_num", data=EMA_Data, lag=1)
##Make Part into a factor variable for early and late
EMA_Data$week_type <- EMA_Data$week_type-1
EMA_Data$Week_Type <- factor(EMA_Data$week_type, levels=c('0','1'),
                         labels=c('Control','Stress'))

3 Descriptives Stats

Before running any stats, we should take a look at some descriptive stats to get an overall feel of our data.

3.1 Compliance Rates

Lets first check compliance rates to see how well our subjects adhered to the sampling. We first check the compliance rates uncorrected for the time at which they were acquired, followed by correction of the time limits. We set this to 1 hour since we only have 6 surveys, and our subjects had varying time schedules. It is indeed a limitation, but we had to do this for methodological reasons.

Uncorrected Compliance

Compliance rates uncorrected for time off-sets

# Recod compliance variable
EMA_Data$completed[EMA_Data$survey_progress==100] <- 1 
Unknown or uninitialised column: `completed`.
# Per subject
calc.nomiss(completed, castor_record_id, data=EMA_Data, prop=T)
  sub_001   sub_002   sub_003   sub_004   sub_005   sub_006   sub_007   sub_008   sub_009   sub_010   sub_011   sub_012   sub_013   sub_014   sub_015 
0.9759036 0.8902439 0.9259259 0.8148148 0.9259259 1.0000000 0.9518072 0.9135802 0.9880952 0.6125000 1.0000000 0.9756098 0.9880952 0.9756098 0.6835443 
  sub_016   sub_017   sub_018   sub_019   sub_020   sub_021   sub_022   sub_023   sub_024   sub_025   sub_026   sub_027   sub_028   sub_029   sub_030 
1.0000000 0.8421053 0.7307692 0.9759036 0.9113924 0.8734177 0.9113924 0.9759036 0.9879518 0.9487179 0.9878049 0.9500000 0.9753086 0.9240506 0.9480519 
  sub_031   sub_032   sub_033   sub_034   sub_035   sub_036   sub_037   sub_038   sub_039   sub_040   sub_043   sub_044   sub_045   sub_046   sub_047 
0.8271605 0.7887324 0.9210526 0.9240506 0.9382716 0.9375000 0.9743590 0.6562500 0.9878049 0.9506173 0.9638554 0.9518072 0.9166667 0.9634146 0.9382716 
  sub_048   sub_050   sub_052   sub_053   sub_054   sub_057   sub_058   sub_059   sub_060   sub_061   sub_062   sub_063   sub_064   sub_065   sub_066 
0.8795181 0.9350649 0.9500000 0.8974359 0.9390244 0.9375000 0.9506173 0.9629630 0.9500000 1.0000000 1.0000000 0.8947368 0.9634146 0.9880952 0.9759036 
  sub_067   sub_068   sub_069   sub_070   sub_071   sub_072   sub_073   sub_074   sub_075   sub_076   sub_077   sub_078   sub_081   sub_082   sub_083 
1.0000000 0.9761905 0.8028169 0.9367089 0.9625000 0.9125000 0.9350649        NA 0.9761905 0.9879518 0.9518072 1.0000000 0.9880952 0.8780488 0.8170732 
  sub_084   sub_085   sub_086   sub_087   sub_088   sub_089   sub_105   sub_115   sub_141   sub_142   sub_149   sub_151   sub_153   sub_155   sub_156 
0.8571429        NA        NA        NA        NA        NA 0.7230769 1.0000000 0.9880952 0.9629630 0.9200000 1.0000000        NA 0.8400000 0.9200000 
  sub_161 
       NA 
# more summary statistics for compliance
summary(calc.nomiss(completed, castor_record_id, data=EMA_Data, prop=TRUE))
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
 0.6125  0.9119  0.9500  0.9249  0.9759  1.0000       8 

Without correcting for time offsets, our EMA measures seem to be nice. Lets see if I correct for timing if it makes a difference next what will happen. We will give participant one hour to finish the survey. If they dont finish it in that time window, we will count it as missing.

Corrected Compliance

Compliance rates correcting for time of completion. first drop any survey that is not complete more than 80%. I then create a variabe that tells as when the survey was completed in terms of time (not date). I then conditionally set the completion variable to zero if the survey does not fall within the completed time window given the beep.

# Set up some stuff for replace and refill
EMA_Data$survey_completed_on <- as.character(EMA_Data$survey_completed_on)
EMA_Data$survey_completed_time <- as.ITime(EMA_Data$survey_completed_on)
EMA_Data$completed[EMA_Data$survey_progress < 80] <- 0 
# Replace and refill conditionals for completion, factoring times
EMA_Data$completed[EMA_Data$survey_completed_time >= (as.ITime("10:30:00")) & EMA_Data$ema_beep==1] <- 0
EMA_Data$completed[EMA_Data$survey_completed_time >= (as.ITime("13:00:00")) & EMA_Data$ema_beep==2] <- 0
EMA_Data$completed[EMA_Data$survey_completed_time >= (as.ITime("15:30:00")) & EMA_Data$ema_beep==3] <- 0
EMA_Data$completed[EMA_Data$survey_completed_time >= (as.ITime("18:00:00")) & EMA_Data$ema_beep==4] <- 0
EMA_Data$completed[EMA_Data$survey_completed_time >= (as.ITime("20:30:00")) & EMA_Data$ema_beep==5] <- 0
EMA_Data$completed[EMA_Data$survey_completed_time >= (as.ITime("23:00:00")) & EMA_Data$ema_beep==6] <- 0
# Reformat 0 to Nan, and get new completion rates
EMA_Data$completed[EMA_Data$completed == 0] <- NA
calc.nomiss(completed, castor_record_id, data=EMA_Data,prop=TRUE)
  sub_001   sub_002   sub_003   sub_004   sub_005   sub_006   sub_007   sub_008   sub_009   sub_010   sub_011   sub_012   sub_013   sub_014   sub_015 
0.9638554 0.7073171 0.7160494 0.6913580 0.9259259 0.9761905 0.9277108 0.8395062 0.9404762 0.5625000 0.8641975 0.9512195 0.9404762 0.7682927 0.4050633 
  sub_016   sub_017   sub_018   sub_019   sub_020   sub_021   sub_022   sub_023   sub_024   sub_025   sub_026   sub_027   sub_028   sub_029   sub_030 
0.9404762 0.8421053 0.7051282 0.9277108 0.8734177 0.7721519 0.8101266 0.9638554 0.9879518 0.9487179 0.9756098 0.9375000 0.9506173 0.9240506 0.9480519 
  sub_031   sub_032   sub_033   sub_034   sub_035   sub_036   sub_037   sub_038   sub_039   sub_040   sub_043   sub_044   sub_045   sub_046   sub_047 
0.8271605 0.7887324 0.8815789 0.8354430 0.9259259 0.9250000 0.9615385 0.4687500 0.8658537 0.9382716 0.9518072 0.9397590 0.7976190 0.9390244 0.9382716 
  sub_048   sub_050   sub_052   sub_053   sub_054   sub_057   sub_058   sub_059   sub_060   sub_061   sub_062   sub_063   sub_064   sub_065   sub_066 
0.8795181 0.8961039 0.9500000 0.8717949 0.9268293 0.9375000 0.9506173 0.9259259 0.9375000 0.9523810 1.0000000 0.8815789 0.9146341 0.9166667 0.9397590 
  sub_067   sub_068   sub_069   sub_070   sub_071   sub_072   sub_073   sub_074   sub_075   sub_076   sub_077   sub_078   sub_081   sub_082   sub_083 
0.9285714 0.6428571 0.5492958 0.7721519 0.9125000 0.8500000 0.7922078        NA 0.9404762 0.8915663 0.9156627 0.8809524 0.9404762 0.8048780 0.7317073 
  sub_084   sub_085   sub_086   sub_087   sub_088   sub_089   sub_105   sub_115   sub_141   sub_142   sub_149   sub_151   sub_153   sub_155   sub_156 
0.8571429        NA        NA        NA        NA        NA 0.7076923 0.8780488 0.8452381 0.9629630 0.8400000 0.9642857        NA 0.6133333 0.9200000 
  sub_161 
       NA 
summary(calc.nomiss(completed, castor_record_id, data=EMA_Data,prop=TRUE))
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
 0.4051  0.8313  0.9157  0.8638  0.9405  1.0000       8 

When we correct for the timing, we actually still have decent completion rates.

3.2 Populations Descriptives

For the population descriptives, we use a different dataframe. So we oresent them below:

Sex

describe(EMA_descr$Sex)
EMA_descr$Sex 
       n  missing distinct 
      83        0        2 
                        
Value      Female   Male
Frequency      51     32
Proportion  0.614  0.386

Contraceptive Use

describe(factor(EMA_descr$Contraceptive_use))
factor(EMA_descr$Contraceptive_use) 
       n  missing distinct 
      83        0        4 
                                  
Value          c  Male    No   Yes
Frequency      8    32    19    24
Proportion 0.096 0.386 0.229 0.289

Program

describe((EMA_descr$Program))
(EMA_descr$Program) 
       n  missing distinct 
      83        0        2 
                                
Value      BSc_BioMed    BSc_Med
Frequency          22         61
Proportion      0.265      0.735

First Week

describe(EMA_descr$First_Week)
EMA_descr$First_Week 
       n  missing distinct 
      83        0        2 
                                      
Value      Control-First    Exam-First
Frequency             56            27
Proportion         0.675         0.325

Days Between Weeks

# Number of days between weeks
summary(abs(EMA_descr$Column1))
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  10.00   14.00   15.00   15.96   16.00   33.00 

Survey Disruption

psych::describe(EMA_Data$physical_disruption)

3.3 Physiology Descriptives

After getting the population descriptives, we should next derive some E4 Quality measures. A lot of the data which is poor quality is already removed early on in the preprocessing pipeline. Instead we can check how many recordings were captured for the IBI data, and the overall movement during testing.

IBI Based Quality

This is a measure of the total duration of IBI’s detected in our windows.

ggplot(EMA_Data, aes(x=ibi_based_quality, colour=ibi_based_quality)) + geom_histogram()

count(EMA_Data$ibi_based_quality > 0.3)
mean(EMA_Data$ibi_based_quality, na.rm=T)
[1] 0.2728208

IBI and ACC

Next we will check if the IBI quality is related to the ACC data. This gives us a good idea of how much motion is affecting our data.

ggplot(EMA_Data, aes(x=ibi_based_quality, y=acc_delta)) + geom_smooth(method="lm", fullrange=F ) + coord_cartesian(ylim = c(0,10), xlim=c(0, 2.5))  + ggtheme + theme(axis.ticks.y=element_line(size=1), axis.text.y = element_text(size=12)) + ylab("ACC Delta") + xlab ("IBI Based Quality")

IBI Quality and HR SD

ggplot(EMA_Data, aes(x=ibi_based_quality, y=hr_sd)) + geom_smooth(method="lm", fullrange=F ) + ggtheme + theme(axis.ticks.y=element_line(size=1), axis.text.y = element_text(size=12)) + ylab("HR SD") + xlab ("IBI Based Quality")

summary(lm(ibi_based_quality ~ hr_sd, data=EMA_Data))

Call:
lm(formula = ibi_based_quality ~ hr_sd, data = EMA_Data)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.42489 -0.16350 -0.05393  0.11612  1.45938 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.473229   0.005947   79.58   <2e-16 ***
hr_sd       -0.024096   0.000601  -40.09   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2211 on 4709 degrees of freedom
  (1912 observations deleted due to missingness)
Multiple R-squared:  0.2545,    Adjusted R-squared:  0.2543 
F-statistic:  1607 on 1 and 4709 DF,  p-value: < 2.2e-16

SC and ACC

Next we will check if the SC signals are related to the ACC. Basically this is just doing explorartory analysis to double check certain things we already expect in our data.

fig.sc_tonic <- ggplot(EMA_Data, aes(x=sc_tonic_mean, y=acc_delta)) + geom_smooth(method="lm", fullrange=F )   + ggtheme + theme(axis.ticks.y=element_line(size=1), axis.text.y = element_text(size=12)) + ylab("ACC Delta") + xlab ("SC Tonic")  
fig.sc_mag <- ggplot(EMA_Data, aes(x=sc_phasic_mag, y=acc_delta)) + geom_smooth(method="lm", fullrange=F )   + ggtheme + theme(axis.ticks.y=element_line(size=1)) + xlab ("SC Mag") 
fig.sc_num <- ggplot(EMA_Data, aes(x=sc_phasic_num, y=acc_delta)) + geom_smooth(method="lm", fullrange=F )   + ggtheme + theme(axis.ticks.y=element_line(size=1)) + xlab ("SC Num") 
fig.sc_auc <- ggplot(EMA_Data, aes(x=sc_phasic_auc, y=acc_delta)) + geom_smooth(method="lm", fullrange=F )   + ggtheme + theme(axis.ticks.y=element_line(size=1)) +  xlab ("SC AUC") 
fig.sc_dur <- ggplot(EMA_Data, aes(x=sc_phasic_dur, y=acc_delta)) + geom_smooth(method="lm", fullrange=F )   + ggtheme + theme(axis.ticks.y=element_line(size=1)) + xlab ("SC Dur")  
fig.temp_mean <- ggplot(EMA_Data, aes(x=physical_excercise_dur, y=acc_delta, colour="red")) + geom_smooth(method="lm") + ggtheme 
ggarrange(fig.sc_tonic, fig.sc_mag, fig.sc_num, fig.sc_auc, fig.sc_dur, fig.temp_mean)
`geom_smooth()` using formula 'y ~ x'
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Removed 1752 rows containing non-finite values (stat_smooth).`geom_smooth()` using formula 'y ~ x'
Removed 1752 rows containing non-finite values (stat_smooth).`geom_smooth()` using formula 'y ~ x'
Removed 1513 rows containing non-finite values (stat_smooth).

3.5 Aggregate Stress

After plotting our variables over all the week, it will be interesting to check the aggregate stress changes, and how each subjects stress reactivity looks like. For this, I will make an average dataframe across the week, so we can look at the average change in mood.

 
#Average Stress per Week:
EMA_avg <- EMA_Data
# Now I can do some merging
EMA_avg <- aggregate(EMA_avg, by=list(EMA_avg$castor_record_id, EMA_avg$Week_Type), FUN=mean, na.rm=T, na.warn=F)
EMA_avg$castor_record_id <- EMA_avg$Group.1
EMA_avg$Week_Type <- EMA_avg$Group.2
EMA_avg$Week_Type <- factor(EMA_avg$Week_Type, levels=c('Control','Stress'),
                     labels=c('Control','Exam'))
# Split the averaged DF to control and stress week
EMA_avg_exam <- subset(EMA_avg, Week_Type=="Exam") 
EMA_avg_control <- subset(EMA_avg, Week_Type!="Exam") 
# Merge by week to calculate change
EMA_avg_wide <-  merge(EMA_avg_exam, EMA_avg_control, by='castor_record_id', suffixes=c('_exam', '_control'))
# Make Aggregated variables 
EMA_avg_wide$mood_positive <-((EMA_avg_wide$mood_positive_control + EMA_avg_wide$mood_positive_exam)/2)
EMA_avg_wide$mood_negative <-((EMA_avg_wide$mood_negative_control + EMA_avg_wide$mood_negative_exam)/2)
EMA_avg_wide$activity_tot <-((EMA_avg_wide$activity_tot_control + EMA_avg_wide$activity_tot_exam)/2)
EMA_avg_wide$social_tot <-((EMA_avg_wide$social_tot_control + EMA_avg_wide$social_tot_exam)/2)
EMA_avg_wide$event_tot <-((EMA_avg_wide$event_tot_control + EMA_avg_wide$event_tot_exam)/2)
EMA_avg_wide$physical_tot <-((EMA_avg_wide$physical_tot_control + EMA_avg_wide$physical_tot_exam)/2)
# Make stress change, and mean centrer it
EMA_avg_wide$stress_reactivity <- EMA_avg_wide$mean_stress_exam - EMA_avg_wide$mean_stress_control
EMA_avg_wide$stress_reactivity_c <- EMA_avg_wide$mean_stress_c_exam - EMA_avg_wide$mean_stress_c_control
EMA_avg_wide$stress_reactivity_z <- scale(EMA_avg_wide$stress_reactivity, center = TRUE, scale = TRUE)

Mean Change in Stress

#Box Plot
mean_box <- ggplot(EMA_avg, aes(y=mean_stress, x=Week_Type, colour=Week_Type,fill=Week_Type, na.rm = TRUE)) +
  geom_boxplot(alpha=1/2) + geom_jitter(width=0.1, alpha=1/2)+
  scale_y_continuous()+ scale_x_discrete()+
  ggtitle("Stress Levels per Week")+
  xlab("") + ylab("Aggregated stress measure\n")+ ggtheme
mean_box + coord_fixed(ratio=1.5)

Stress Rectivity Heat Plot

scat_str <- ggplot (EMA_avg_wide, aes(y=stress_reactivity_c, x=factor(1), colour=stress_reactivity_c) ) +
    geom_jitter( width = 0.25, alpha=0.75, size = 2) +
    ggtitle("Individual Stress Reactivity to Exams\n")+ylab("Stress Reactivity\n")+labs(color = "Stress Reactivity\n")+
    theme(text=element_text(size=18,  family="Cambria"),
        plot.title=element_text (size=20, hjust=0.5),
        axis.title.x=element_blank(),axis.text.x=element_blank(),axis.ticks.x=element_blank(),
        axis.text.y = element_text(size=18),axis.title.y=element_text(size=18),
        panel.background = element_rect(fill="white"),
        panel.grid.minor.y = element_line(size=3),
        panel.grid.major = element_line(colour = "aliceblue"))
  scat_str + scale_color_gradient(low="blue", high="red") + coord_fixed(ratio = 0.6)

4 Inferential Stats

Now we can do some statistical modeling with inferential stats. We use different glmer models for our data. The method used it simple: We fit the model multiple times with different families of models and different links. Based on the AIC, and the residuals, we pick the best fitting model. Additionally, we use a maximal fit approach. For our main fixed effect of interest, I also model a random slope and ranom intercept. For other covariates, I model them as fixed effects with random slopes and a fixed intercept. Subject is used as a random effect in all our models.

4.1 Week vs Week Differences

First we test our paradigm, and see whether it also has effects on our outcome measures of mood and physiological arousal. We check for main effects of week type (control or stress) on the variables. We also model covariates: Sex, Program, activity levels, and survey instance

4.1.1 Subjective Stress

Here we test the confirmatory analysis. We expect to see increased subjective stress in the stress week, which is confirmed in the models. For simplicity, we only present the final model selected based on the optimal fit.

Social Stress

# Model
glmer.social_week <- glmer( social_tot_s ~ Week_Type +  #Model week
    Sex + Program +  # Model sex and program 
    First_Week + ema_day*ema_beep_f + # Model day related items
    acc_delta +  physical_excercise_dur + acc_delta*physical_excercise_dur + # Model movement
    (1+Week_Type|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (0+ema_survey|castor_record_id) + (0+physical_excercise_dur|castor_record_id) + 
    (1|castor_record_id:ema_day:ema_beep_f),
    data=EMA_Data,
    family=Gamma(link="log"),
    control=glmerControl(calc.derivs = FALSE))
failure to converge in 10000 evaluations
# Model Summary
summary(glmer.social_week)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( log )
Formula: social_tot_s ~ Week_Type + Sex + Program + First_Week + ema_day *      ema_beep_f + acc_delta + physical_excercise_dur + acc_delta *  
    physical_excercise_dur + (1 + Week_Type | castor_record_id) +      (0 + acc_delta | castor_record_id) + (0 + ema_survey | castor_record_id) +  
    (0 + physical_excercise_dur | castor_record_id) + (1 | castor_record_id:ema_day:ema_beep_f)
   Data: EMA_Data
Control: glmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 16638.0  17010.7  -8262.0  16524.0     5053 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.2149 -0.6006 -0.0368  0.5755  3.7796 

Random effects:
 Groups                              Name                   Variance  Std.Dev. Corr 
 castor_record_id.ema_day.ema_beep_f (Intercept)            4.659e-02 0.215843      
 castor_record_id                    physical_excercise_dur 4.829e-02 0.219758      
 castor_record_id.1                  ema_survey             3.832e-06 0.001958      
 castor_record_id.2                  acc_delta              2.804e-05 0.005295      
 castor_record_id.3                  (Intercept)            8.948e-03 0.094593      
                                     Week_TypeStress        1.305e-02 0.114225 -0.54
 Residual                                                   7.285e-02 0.269912      
Number of obs: 5110, groups:  castor_record_id:ema_day:ema_beep_f, 3069; castor_record_id, 82

Fixed effects:
                                   Estimate Std. Error t value Pr(>|z|)    
(Intercept)                       1.4459071  0.0433969  33.318  < 2e-16 ***
Week_TypeStress                   0.0231669  0.0150962   1.535 0.124876    
SexMale                           0.0760746  0.0240128   3.168 0.001534 ** 
ProgramBSc_Med                    0.0115562  0.0263702   0.438 0.661221    
First_WeekExam-First              0.0285138  0.0246666   1.156 0.247694    
ema_dayEMA 2.                    -0.0693930  0.0494415  -1.404 0.160456    
ema_dayEMA 3.                    -0.0899728  0.0504051  -1.785 0.074263 .  
ema_dayEMA 4.                    -0.0570609  0.0504950  -1.130 0.258463    
ema_dayEMA 5.                    -0.0534526  0.0502936  -1.063 0.287868    
ema_dayEMA 6.                    -0.0582426  0.0514455  -1.132 0.257583    
ema_dayEMA 7.                    -0.0506983  0.0522094  -0.971 0.331520    
ema_beep_f2                      -0.0446500  0.0493767  -0.904 0.365851    
ema_beep_f3                      -0.0744811  0.0489327  -1.522 0.127981    
ema_beep_f4                      -0.1250187  0.0492459  -2.539 0.011128 *  
ema_beep_f5                      -0.2118627  0.0517289  -4.096 4.21e-05 ***
ema_beep_f6                      -0.1779153  0.0500260  -3.556 0.000376 ***
acc_delta                        -0.0014102  0.0012080  -1.167 0.243060    
physical_excercise_dur           -0.0691517  0.0552336  -1.252 0.210575    
ema_dayEMA 2.:ema_beep_f2         0.0526487  0.0690752   0.762 0.445945    
ema_dayEMA 3.:ema_beep_f2         0.0315905  0.0704740   0.448 0.653967    
ema_dayEMA 4.:ema_beep_f2         0.0257847  0.0707370   0.365 0.715473    
ema_dayEMA 5.:ema_beep_f2        -0.0211809  0.0698265  -0.303 0.761633    
ema_dayEMA 6.:ema_beep_f2         0.0114780  0.0703360   0.163 0.870371    
ema_dayEMA 7.:ema_beep_f2         0.0517057  0.0723283   0.715 0.474686    
ema_dayEMA 2.:ema_beep_f3         0.0688701  0.0693993   0.992 0.321015    
ema_dayEMA 3.:ema_beep_f3         0.0710524  0.0697697   1.018 0.308495    
ema_dayEMA 4.:ema_beep_f3         0.0333682  0.0702251   0.475 0.634673    
ema_dayEMA 5.:ema_beep_f3         0.0397527  0.0695774   0.571 0.567766    
ema_dayEMA 6.:ema_beep_f3         0.0488674  0.0703312   0.695 0.487169    
ema_dayEMA 7.:ema_beep_f3         0.0940237  0.0709967   1.324 0.185390    
ema_dayEMA 2.:ema_beep_f4         0.1055622  0.0695685   1.517 0.129170    
ema_dayEMA 3.:ema_beep_f4         0.0800582  0.0697799   1.147 0.251260    
ema_dayEMA 4.:ema_beep_f4         0.0534222  0.0701447   0.762 0.446299    
ema_dayEMA 5.:ema_beep_f4         0.0626509  0.0699905   0.895 0.370715    
ema_dayEMA 6.:ema_beep_f4         0.0936408  0.0709948   1.319 0.187176    
ema_dayEMA 7.:ema_beep_f4         0.0651922  0.0721821   0.903 0.366440    
ema_dayEMA 2.:ema_beep_f5         0.0723306  0.0711287   1.017 0.309202    
ema_dayEMA 3.:ema_beep_f5         0.1093111  0.0725282   1.507 0.131771    
ema_dayEMA 4.:ema_beep_f5         0.0962671  0.0721599   1.334 0.182178    
ema_dayEMA 5.:ema_beep_f5         0.0774565  0.0736190   1.052 0.292741    
ema_dayEMA 6.:ema_beep_f5         0.0975232  0.0741163   1.316 0.188236    
ema_dayEMA 7.:ema_beep_f5         0.1085866  0.0736165   1.475 0.140204    
ema_dayEMA 2.:ema_beep_f6         0.0348453  0.0702225   0.496 0.619744    
ema_dayEMA 3.:ema_beep_f6         0.0456472  0.0706539   0.646 0.518235    
ema_dayEMA 4.:ema_beep_f6        -0.0008737  0.0706302  -0.012 0.990130    
ema_dayEMA 5.:ema_beep_f6         0.0442189  0.0705725   0.627 0.530939    
ema_dayEMA 6.:ema_beep_f6         0.0928045  0.0724378   1.281 0.200137    
ema_dayEMA 7.:ema_beep_f6         0.1209466  0.0800214   1.511 0.130680    
acc_delta:physical_excercise_dur -0.0089227  0.0067757  -1.317 0.187884    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 49 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
convergence code: 0
failure to converge in 10000 evaluations

Physical Stress

# Model
glmer.physical_week<- glmer( physical_tot_s ~ Week_Type +  #Model week
    Sex + Program +  # Model sex and program 
    First_Week + ema_day*ema_beep_f + # Model day related items
    acc_delta +  physical_excercise_dur + acc_delta*physical_excercise_dur + # Model movement
    (1+Week_Type|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (0+ema_survey|castor_record_id) + (0+physical_excercise_dur|castor_record_id) + 
    (1|castor_record_id:ema_day:ema_beep_f),
    data=EMA_Data,
    #family=Gamma,
    control=lmerControl(calc.derivs = FALSE))
# Model Summary
summary(glmer.physical_week)
Linear mixed model fit by REML ['lmerMod']
Formula: physical_tot_s ~ Week_Type + Sex + Program + First_Week + ema_day *      ema_beep_f + acc_delta + physical_excercise_dur + acc_delta *  
    physical_excercise_dur + (1 + Week_Type | castor_record_id) +      (0 + acc_delta | castor_record_id) + (0 + ema_survey | castor_record_id) +  
    (0 + physical_excercise_dur | castor_record_id) + (1 | castor_record_id:ema_day:ema_beep_f)
   Data: EMA_Data
Control: lmerControl(calc.derivs = FALSE)

REML criterion at convergence: 16810.1

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.5099 -0.6493 -0.0581  0.5893  5.4381 

Random effects:
 Groups                              Name                   Variance  Std.Dev. Corr 
 castor_record_id.ema_day.ema_beep_f (Intercept)            0.0426767 0.20658       
 castor_record_id                    physical_excercise_dur 0.0363058 0.19054       
 castor_record_id.1                  ema_survey             0.0007335 0.02708       
 castor_record_id.2                  acc_delta              0.0000000 0.00000       
 castor_record_id.3                  (Intercept)            0.8433427 0.91834       
                                     Week_TypeStress        0.6104499 0.78131  -0.34
 Residual                                                   1.3327886 1.15446       
Number of obs: 5110, groups:  castor_record_id:ema_day:ema_beep_f, 3069; castor_record_id, 82

Fixed effects:
                                   Estimate Std. Error t value
(Intercept)                       4.5630564  0.2391308  19.082
Week_TypeStress                  -0.0620684  0.0931086  -0.667
SexMale                          -0.2994700  0.2088982  -1.434
ProgramBSc_Med                   -0.0605230  0.2293859  -0.264
First_WeekExam-First              0.2777947  0.2143295   1.296
ema_dayEMA 2.                    -0.1915930  0.1502740  -1.275
ema_dayEMA 3.                     0.0342863  0.1567591   0.219
ema_dayEMA 4.                    -0.2060100  0.1628749  -1.265
ema_dayEMA 5.                    -0.4123216  0.1687553  -2.443
ema_dayEMA 6.                    -0.2288882  0.1791044  -1.278
ema_dayEMA 7.                    -0.4521119  0.1907229  -2.371
ema_beep_f2                      -0.2055534  0.1487070  -1.382
ema_beep_f3                      -0.2976639  0.1477558  -2.015
ema_beep_f4                      -0.0009249  0.1487246  -0.006
ema_beep_f5                      -0.8137608  0.1581781  -5.145
ema_beep_f6                      -0.6040162  0.1527357  -3.955
acc_delta                        -0.0148329  0.0034458  -4.305
physical_excercise_dur            0.5563173  0.1682507   3.306
ema_dayEMA 2.:ema_beep_f2         0.0228770  0.2071262   0.110
ema_dayEMA 3.:ema_beep_f2        -0.0906231  0.2118184  -0.428
ema_dayEMA 4.:ema_beep_f2        -0.1270573  0.2141211  -0.593
ema_dayEMA 5.:ema_beep_f2         0.1538572  0.2112295   0.728
ema_dayEMA 6.:ema_beep_f2        -0.0631026  0.2120423  -0.298
ema_dayEMA 7.:ema_beep_f2         0.1628191  0.2181488   0.746
ema_dayEMA 2.:ema_beep_f3         0.1771502  0.2086052   0.849
ema_dayEMA 3.:ema_beep_f3        -0.2428685  0.2100991  -1.156
ema_dayEMA 4.:ema_beep_f3        -0.0354755  0.2125094  -0.167
ema_dayEMA 5.:ema_beep_f3         0.2196079  0.2103857   1.044
ema_dayEMA 6.:ema_beep_f3        -0.1684959  0.2119922  -0.795
ema_dayEMA 7.:ema_beep_f3         0.0989181  0.2147959   0.461
ema_dayEMA 2.:ema_beep_f4         0.0281753  0.2095475   0.134
ema_dayEMA 3.:ema_beep_f4        -0.2938972  0.2099347  -1.400
ema_dayEMA 4.:ema_beep_f4        -0.0870502  0.2119519  -0.411
ema_dayEMA 5.:ema_beep_f4         0.2754781  0.2121629   1.298
ema_dayEMA 6.:ema_beep_f4        -0.2109497  0.2146426  -0.983
ema_dayEMA 7.:ema_beep_f4         0.2532508  0.2191286   1.156
ema_dayEMA 2.:ema_beep_f5         0.1758335  0.2151572   0.817
ema_dayEMA 3.:ema_beep_f5        -0.0102118  0.2211402  -0.046
ema_dayEMA 4.:ema_beep_f5         0.0742144  0.2194411   0.338
ema_dayEMA 5.:ema_beep_f5         0.5792033  0.2254355   2.569
ema_dayEMA 6.:ema_beep_f5         0.2731363  0.2254783   1.211
ema_dayEMA 7.:ema_beep_f5         0.4974208  0.2252814   2.208
ema_dayEMA 2.:ema_beep_f6         0.1841992  0.2129285   0.865
ema_dayEMA 3.:ema_beep_f6        -0.1726791  0.2145978  -0.805
ema_dayEMA 4.:ema_beep_f6        -0.0806420  0.2146432  -0.376
ema_dayEMA 5.:ema_beep_f6         0.3063814  0.2148430   1.426
ema_dayEMA 6.:ema_beep_f6         0.3308938  0.2201258   1.503
ema_dayEMA 7.:ema_beep_f6         0.3920681  0.2480267   1.581
acc_delta:physical_excercise_dur -0.0143489  0.0229982  -0.624

Correlation matrix not shown by default, as p = 49 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it

Table and Plot

To make things readable, we present the results in a simpler table. Additionally, we also present a plot for visualization. This is the same plot that is presented in our paper as figure 2.

tab_model(glmer.event_week, glmer.activity_week,  glmer.social_week, glmer.physical_week, 
           terms=c("(Intercept)","Week_Type [Stress]", "Sex [Male]", "Program [BSc_Med]", "First_Week [Exam-First]", "acc_delta", "physical_excercise_dur"), 
          dv.labels=c("Event", "Activity", "Social", "Physical"), 
          title="Table 1. Subjective Stress vs Week Type", show.df=T, show.fstat = T,
          transform=NULL, 
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
Table 1. Subjective Stress vs Week Type
  Event Activity Social Physical
Predictors Estimates std. Error CI Statistic p df Estimates std. Error CI Statistic p df Estimates std. Error CI Statistic p df Estimates std. Error CI Statistic p df
(Intercept) 5.59 0.14 5.31 – 5.86 39.95 <0.001 5053.00 3.96 0.23 3.50 – 4.41 17.06 <0.001 5053.00 1.45 0.04 1.36 – 1.53 33.32 <0.001 5053.00 4.56 0.24 4.09 – 5.03 19.08 <0.001 5053.00
Week_Type [Stress] 0.30 0.06 0.18 – 0.42 4.92 <0.001 5053.00 0.47 0.10 0.27 – 0.67 4.71 <0.001 5053.00 0.02 0.02 -0.01 – 0.05 1.53 0.125 5053.00 -0.06 0.09 -0.24 – 0.12 -0.67 0.505 5053.00
Sex [Male] 0.00 0.09 -0.17 – 0.17 0.01 0.989 5053.00 -0.04 0.15 -0.34 – 0.26 -0.24 0.812 5053.00 0.08 0.02 0.03 – 0.12 3.17 0.002 5053.00 -0.30 0.21 -0.71 – 0.11 -1.43 0.152 5053.00
Program [BSc_Med] 0.01 0.10 -0.18 – 0.20 0.11 0.914 5053.00 0.03 0.17 -0.30 – 0.36 0.16 0.873 5053.00 0.01 0.03 -0.04 – 0.06 0.44 0.661 5053.00 -0.06 0.23 -0.51 – 0.39 -0.26 0.792 5053.00
First_Week [Exam-First] -0.08 0.09 -0.25 – 0.10 -0.87 0.386 5053.00 0.08 0.16 -0.23 – 0.38 0.48 0.631 5053.00 0.03 0.02 -0.02 – 0.08 1.16 0.248 5053.00 0.28 0.21 -0.14 – 0.70 1.30 0.195 5053.00
acc_delta -0.00 0.00 -0.01 – 0.01 -0.22 0.824 5053.00 -0.00 0.01 -0.01 – 0.01 -0.20 0.843 5053.00 -0.00 0.00 -0.00 – 0.00 -1.17 0.243 5053.00 -0.01 0.00 -0.02 – -0.01 -4.30 <0.001 5053.00
physical_excercise_dur -0.30 0.17 -0.62 – 0.03 -1.78 0.075 5053.00 0.15 0.25 -0.35 – 0.65 0.59 0.556 5053.00 -0.07 0.06 -0.18 – 0.04 -1.25 0.211 5053.00 0.56 0.17 0.23 – 0.89 3.31 0.001 5053.00
Random Effects
σ2       1.33
τ00       0.04 castor_record_id.ema_day.ema_beep_f
      0.04 castor_record_id
      0.00 castor_record_id.1
      0.00 castor_record_id.2
      0.84 castor_record_id.3
τ11       0.61 castor_record_id.3.Week_TypeStress
ρ01       -0.34 castor_record_id.3
N 82 castor_record_id 82 castor_record_id 82 castor_record_id 82 castor_record_id
7 ema_day 7 ema_day 7 ema_day 7 ema_day
6 ema_beep_f 6 ema_beep_f 6 ema_beep_f 6 ema_beep_f
Observations 5110 5110 5110 5110
Marginal R2 / Conditional R2 NA NA NA 0.080 / NA

In the plot, we can see an increase in subjective stress measures for both event and activity realted stress during the exam week.

# Subset the variables we want to plot
plot.mood_week <- plot_models(glmer.event_week, glmer.activity_week, glmer.social_week, glmer.physical_week)
rm_term <- as.vector(plot.mood_week$data$term[1:length(plot.mood_week$data$term)])
rm_term <- rm_term[rm_term != "Week_TypeStress"]
# Make the plot
plot.mood_week <- plot_models(glmer.event_week, glmer.activity_week, glmer.social_week, glmer.physical_week,
                                  m.labels=c("Event Stress", "Activity Stress","Social Stress", "Physical Stress" ),
                                  axis.labels = c(" "),
                                # Stastistical Stuff
                                rm.terms = rm_term,
                                show.p=T,
                                p.shape=T,
                                legend.pval.title = "Significance", 
                                # Visual Stuff
                                colors="#666666",
                                dot.size=2,
                                line.size = 1,
                                spacing=1 , 
                                vline.color = "darkgrey", 
                                legend.title = "") + ylab("\nParameter Estimate (a.u.)") + xlab("Subjective Stress") + 
                                ptheme + 
                                theme(axis.ticks.y=element_blank(), 
                                      legend.text=element_text(size=16), legend.title = element_text(size=16),
                                      axis.title = element_text(size=16),axis.text.x=element_text(size=11),
                                      panel.grid.major.x = element_line(colour = "grey95"),
                                      panel.grid.minor.x = element_line(colour = "grey90")) 
# Show and save
plot.mood_week+ coord_flip(ylim=c(-0.65,0.65)) + theme(panel.grid.major.y = element_line(colour = "grey95"), panel.grid.minor.y = element_line(colour = "grey90"))
Coordinate system already present. Adding new coordinate system, which will replace the existing one.

#ggsave("figures/fig_WeekResid_SubjectiveStress.tiff",units="in", width=4, height=4, dpi=300, compression = 'lzw', bg="transparent")

4.1.2 Mood

Next, we want to look at the mood outcome measures for positive and negative mood. I used the same covariates as before, and the same approach to modeling. That is, I fit all possible families and links, and picked the best fit.

Positive Affect

# Model
glmer.posmood_week <- glmer( mood_positive_s ~ Week_Type +  #Model week
    Sex + Program +  # Model sex and program 
    First_Week + ema_day*ema_beep_f + # Model day related items
    physical_excercise_dur + acc_delta + acc_delta*physical_excercise_dur + # Model movement
    (1+Week_Type|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (0+ema_survey|castor_record_id) + (0+physical_excercise_dur|castor_record_id) + 
    (1|castor_record_id:ema_day:ema_beep_f),
    data=EMA_Data,
    family=gaussian(link="log"),
    control=lmerControl(calc.derivs = FALSE))
# Model Summary
summary(glmer.posmood_week)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: gaussian  ( log )
Formula: mood_positive_s ~ Week_Type + Sex + Program + First_Week + ema_day *      ema_beep_f + physical_excercise_dur + acc_delta + acc_delta *  
    physical_excercise_dur + (1 + Week_Type | castor_record_id) +      (0 + acc_delta | castor_record_id) + (0 + ema_survey | castor_record_id) +  
    (0 + physical_excercise_dur | castor_record_id) + (1 | castor_record_id:ema_day:ema_beep_f)
   Data: EMA_Data
Control: lmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 17272.1  17644.8  -8579.0  17158.1     5053 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.4607 -0.5933  0.0526  0.6165  4.1466 

Random effects:
 Groups                              Name                   Variance  Std.Dev.  Corr 
 castor_record_id.ema_day.ema_beep_f (Intercept)            1.445e-09 3.801e-05      
 castor_record_id                    physical_excercise_dur 7.693e-07 8.771e-04      
 castor_record_id.1                  ema_survey             6.776e-06 2.603e-03      
 castor_record_id.2                  acc_delta              0.000e+00 0.000e+00      
 castor_record_id.3                  (Intercept)            2.993e-02 1.730e-01      
                                     Week_TypeStress        1.444e-02 1.202e-01 -0.17
 Residual                                                   1.486e+00 1.219e+00      
Number of obs: 5110, groups:  castor_record_id:ema_day:ema_beep_f, 3069; castor_record_id, 82

Fixed effects:
                                   Estimate Std. Error t value Pr(>|z|)    
(Intercept)                       1.8231525  0.0444471  41.019  < 2e-16 ***
Week_TypeStress                  -0.0770281  0.0145112  -5.308 1.11e-07 ***
SexMale                           0.0463586  0.0403972   1.148 0.251146    
ProgramBSc_Med                    0.0205102  0.0443852   0.462 0.644013    
First_WeekExam-First             -0.0073609  0.0414660  -0.178 0.859103    
ema_dayEMA 2.                     0.0359134  0.0238576   1.505 0.132241    
ema_dayEMA 3.                    -0.0084395  0.0248825  -0.339 0.734479    
ema_dayEMA 4.                    -0.0002130  0.0253336  -0.008 0.993293    
ema_dayEMA 5.                     0.0065964  0.0257153   0.257 0.797551    
ema_dayEMA 6.                    -0.0129383  0.0266128  -0.486 0.626848    
ema_dayEMA 7.                    -0.0145495  0.0277341  -0.525 0.599855    
ema_beep_f2                       0.0189485  0.0238312   0.795 0.426547    
ema_beep_f3                       0.0310231  0.0235189   1.319 0.187145    
ema_beep_f4                       0.0245266  0.0237311   1.034 0.301362    
ema_beep_f5                       0.0900308  0.0243958   3.690 0.000224 ***
ema_beep_f6                       0.0808752  0.0236408   3.421 0.000624 ***
physical_excercise_dur            0.0633148  0.0249673   2.536 0.011216 *  
acc_delta                         0.0012188  0.0005357   2.275 0.022890 *  
ema_dayEMA 2.:ema_beep_f2        -0.0231506  0.0328963  -0.704 0.481592    
ema_dayEMA 3.:ema_beep_f2         0.0102951  0.0338269   0.304 0.760863    
ema_dayEMA 4.:ema_beep_f2         0.0008838  0.0342634   0.026 0.979421    
ema_dayEMA 5.:ema_beep_f2        -0.0106469  0.0338654  -0.314 0.753227    
ema_dayEMA 6.:ema_beep_f2        -0.0112518  0.0342189  -0.329 0.742293    
ema_dayEMA 7.:ema_beep_f2        -0.0116784  0.0352622  -0.331 0.740503    
ema_dayEMA 2.:ema_beep_f3        -0.0729524  0.0332003  -2.197 0.027996 *  
ema_dayEMA 3.:ema_beep_f3        -0.0184629  0.0336525  -0.549 0.583256    
ema_dayEMA 4.:ema_beep_f3        -0.0021692  0.0339030  -0.064 0.948983    
ema_dayEMA 5.:ema_beep_f3        -0.0259461  0.0336814  -0.770 0.441099    
ema_dayEMA 6.:ema_beep_f3        -0.0102841  0.0339227  -0.303 0.761766    
ema_dayEMA 7.:ema_beep_f3        -0.0572074  0.0349988  -1.635 0.102143    
ema_dayEMA 2.:ema_beep_f4        -0.0299963  0.0331047  -0.906 0.364880    
ema_dayEMA 3.:ema_beep_f4         0.0270369  0.0333674   0.810 0.417780    
ema_dayEMA 4.:ema_beep_f4         0.0049048  0.0338203   0.145 0.884690    
ema_dayEMA 5.:ema_beep_f4        -0.0304746  0.0341575  -0.892 0.372297    
ema_dayEMA 6.:ema_beep_f4        -0.0120031  0.0345190  -0.348 0.728047    
ema_dayEMA 7.:ema_beep_f4        -0.0100683  0.0353250  -0.285 0.775629    
ema_dayEMA 2.:ema_beep_f5        -0.0538986  0.0332010  -1.623 0.104503    
ema_dayEMA 3.:ema_beep_f5        -0.0173217  0.0345140  -0.502 0.615756    
ema_dayEMA 4.:ema_beep_f5        -0.0119120  0.0340266  -0.350 0.726280    
ema_dayEMA 5.:ema_beep_f5        -0.0793808  0.0355805  -2.231 0.025680 *  
ema_dayEMA 6.:ema_beep_f5        -0.0583661  0.0355166  -1.643 0.100311    
ema_dayEMA 7.:ema_beep_f5        -0.0568634  0.0356347  -1.596 0.110549    
ema_dayEMA 2.:ema_beep_f6        -0.0238617  0.0327344  -0.729 0.466033    
ema_dayEMA 3.:ema_beep_f6        -0.0369972  0.0338226  -1.094 0.274016    
ema_dayEMA 4.:ema_beep_f6        -0.0155267  0.0334988  -0.463 0.643007    
ema_dayEMA 5.:ema_beep_f6        -0.0289097  0.0336308  -0.860 0.389999    
ema_dayEMA 6.:ema_beep_f6        -0.0504028  0.0347243  -1.452 0.146637    
ema_dayEMA 7.:ema_beep_f6        -0.0269167  0.0389139  -0.692 0.489127    
physical_excercise_dur:acc_delta -0.0006480  0.0033907  -0.191 0.848432    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 49 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it

Negative Affect

# Model
glmer.negmood_week <- glmer( mood_negative_s ~  Week_Type +  #Model week
    Sex + Program +  # Model sex and program 
    First_Week + ema_day*ema_beep_f + # Model day related items
    physical_excercise_dur + acc_delta + acc_delta*physical_excercise_dur + # Model movement
    (1+Week_Type|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (0+ema_survey|castor_record_id) + (0+physical_excercise_dur|castor_record_id) + 
    (1|castor_record_id:ema_day:ema_beep_f),
    data=EMA_Data,
    family=Gamma(link="log"),
    control=glmerControl(calc.derivs = FALSE))
# Model Summary
summary(glmer.negmood_week) 
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( log )
Formula: mood_negative_s ~ Week_Type + Sex + Program + First_Week + ema_day *      ema_beep_f + physical_excercise_dur + acc_delta + acc_delta *  
    physical_excercise_dur + (1 + Week_Type | castor_record_id) +      (0 + acc_delta | castor_record_id) + (0 + ema_survey | castor_record_id) +  
    (0 + physical_excercise_dur | castor_record_id) + (1 | castor_record_id:ema_day:ema_beep_f)
   Data: EMA_Data
Control: glmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 12044.8  12417.5  -5965.4  11930.8     5053 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.3470 -0.5195 -0.0785  0.4418  5.5713 

Random effects:
 Groups                              Name                   Variance  Std.Dev. Corr 
 castor_record_id.ema_day.ema_beep_f (Intercept)            5.967e-02 0.244280      
 castor_record_id                    physical_excercise_dur 1.009e-01 0.317593      
 castor_record_id.1                  ema_survey             1.501e-05 0.003874      
 castor_record_id.2                  acc_delta              3.028e-05 0.005503      
 castor_record_id.3                  (Intercept)            5.767e-02 0.240153      
                                     Week_TypeStress        3.491e-02 0.186837 -0.46
 Residual                                                   1.011e-01 0.317969      
Number of obs: 5110, groups:  castor_record_id:ema_day:ema_beep_f, 3069; castor_record_id, 82

Fixed effects:
                                  Estimate Std. Error t value Pr(>|z|)    
(Intercept)                       1.031729   0.068715  15.015  < 2e-16 ***
Week_TypeStress                   0.111470   0.022908   4.866 1.14e-06 ***
SexMale                          -0.206435   0.053294  -3.874 0.000107 ***
ProgramBSc_Med                   -0.128917   0.058583  -2.201 0.027767 *  
First_WeekExam-First              0.060818   0.054650   1.113 0.265767    
ema_dayEMA 2.                    -0.208437   0.057197  -3.644 0.000268 ***
ema_dayEMA 3.                    -0.183836   0.058442  -3.146 0.001657 ** 
ema_dayEMA 4.                    -0.194544   0.058761  -3.311 0.000930 ***
ema_dayEMA 5.                    -0.189802   0.058763  -3.230 0.001238 ** 
ema_dayEMA 6.                    -0.173772   0.060399  -2.877 0.004014 ** 
ema_dayEMA 7.                    -0.151262   0.061689  -2.452 0.014206 *  
ema_beep_f2                      -0.033504   0.057054  -0.587 0.557048    
ema_beep_f3                      -0.145839   0.056553  -2.579 0.009914 ** 
ema_beep_f4                      -0.149544   0.056921  -2.627 0.008608 ** 
ema_beep_f5                      -0.241366   0.059861  -4.032 5.53e-05 ***
ema_beep_f6                      -0.300447   0.057901  -5.189 2.11e-07 ***
physical_excercise_dur           -0.062434   0.068910  -0.906 0.364924    
acc_delta                        -0.002835   0.001369  -2.071 0.038367 *  
ema_dayEMA 2.:ema_beep_f2         0.073858   0.079779   0.926 0.354555    
ema_dayEMA 3.:ema_beep_f2         0.053421   0.081423   0.656 0.511763    
ema_dayEMA 4.:ema_beep_f2         0.013499   0.081763   0.165 0.868863    
ema_dayEMA 5.:ema_beep_f2         0.042781   0.080679   0.530 0.595930    
ema_dayEMA 6.:ema_beep_f2         0.022114   0.081258   0.272 0.785511    
ema_dayEMA 7.:ema_beep_f2        -0.009783   0.083580  -0.117 0.906820    
ema_dayEMA 2.:ema_beep_f3         0.189467   0.080187   2.363 0.018136 *  
ema_dayEMA 3.:ema_beep_f3         0.140736   0.080607   1.746 0.080818 .  
ema_dayEMA 4.:ema_beep_f3         0.131434   0.081156   1.620 0.105335    
ema_dayEMA 5.:ema_beep_f3         0.146405   0.080393   1.821 0.068591 .  
ema_dayEMA 6.:ema_beep_f3         0.142722   0.081258   1.756 0.079018 .  
ema_dayEMA 7.:ema_beep_f3         0.206186   0.082048   2.513 0.011971 *  
ema_dayEMA 2.:ema_beep_f4         0.215605   0.080382   2.682 0.007313 ** 
ema_dayEMA 3.:ema_beep_f4         0.124818   0.080617   1.548 0.121552    
ema_dayEMA 4.:ema_beep_f4         0.155289   0.081062   1.916 0.055404 .  
ema_dayEMA 5.:ema_beep_f4         0.174269   0.080886   2.154 0.031201 *  
ema_dayEMA 6.:ema_beep_f4         0.164120   0.082050   2.000 0.045474 *  
ema_dayEMA 7.:ema_beep_f4         0.153902   0.083469   1.844 0.065207 .  
ema_dayEMA 2.:ema_beep_f5         0.233892   0.082226   2.845 0.004448 ** 
ema_dayEMA 3.:ema_beep_f5         0.126813   0.083866   1.512 0.130512    
ema_dayEMA 4.:ema_beep_f5         0.227929   0.083437   2.732 0.006300 ** 
ema_dayEMA 5.:ema_beep_f5         0.237625   0.085158   2.790 0.005264 ** 
ema_dayEMA 6.:ema_beep_f5         0.229316   0.085716   2.675 0.007466 ** 
ema_dayEMA 7.:ema_beep_f5         0.216046   0.085174   2.537 0.011195 *  
ema_dayEMA 2.:ema_beep_f6         0.270713   0.081194   3.334 0.000856 ***
ema_dayEMA 3.:ema_beep_f6         0.274803   0.081712   3.363 0.000771 ***
ema_dayEMA 4.:ema_beep_f6         0.240842   0.081668   2.949 0.003188 ** 
ema_dayEMA 5.:ema_beep_f6         0.294835   0.081609   3.613 0.000303 ***
ema_dayEMA 6.:ema_beep_f6         0.318424   0.083780   3.801 0.000144 ***
ema_dayEMA 7.:ema_beep_f6         0.349228   0.092832   3.762 0.000169 ***
physical_excercise_dur:acc_delta -0.008999   0.007994  -1.126 0.260277    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 49 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
convergence code: 0
failure to converge in 10000 evaluations

Table

Next we present the table of the results. We present a plot later that shows the results for all the outcomes, but for now we simply print the results of the mixed models

tab_model(glmer.posmood_week, glmer.negmood_week,
          terms=c("(Intercept)","Week_Type [Stress]", "Sex [Male]", "Program [BSc_Med]", "First_Week [Exam-First]", "acc_delta", "physical_excercise_dur"), 
          dv.labels=c("Positive", "Negative"), 
          title="Table 2. Mood vs Week Type", 
          transform=NULL, 
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
Table 2. Mood vs Week Type
  Positive Negative
Predictors Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p
(Intercept) 1.82 0.04 1.74 – 1.91 41.02 <0.001 1.03 0.07 0.90 – 1.17 15.01 <0.001
Week_Type [Stress] -0.08 0.01 -0.11 – -0.05 -5.31 <0.001 0.11 0.02 0.07 – 0.16 4.87 <0.001
Sex [Male] 0.05 0.04 -0.03 – 0.13 1.15 0.251 -0.21 0.05 -0.31 – -0.10 -3.87 <0.001
Program [BSc_Med] 0.02 0.04 -0.07 – 0.11 0.46 0.644 -0.13 0.06 -0.24 – -0.01 -2.20 0.028
First_Week [Exam-First] -0.01 0.04 -0.09 – 0.07 -0.18 0.859 0.06 0.05 -0.05 – 0.17 1.11 0.266
physical_excercise_dur 0.06 0.02 0.01 – 0.11 2.54 0.011 -0.06 0.07 -0.20 – 0.07 -0.91 0.365
acc_delta 0.00 0.00 0.00 – 0.00 2.28 0.023 -0.00 0.00 -0.01 – -0.00 -2.07 0.038
Random Effects
σ2 1.49  
τ00 0.00 castor_record_id.ema_day.ema_beep_f  
0.00 castor_record_id  
0.00 castor_record_id.1  
0.00 castor_record_id.2  
0.03 castor_record_id.3  
τ11 0.01 castor_record_id.3.Week_TypeStress  
ρ01 -0.17 castor_record_id.3  
N 82 castor_record_id 82 castor_record_id
7 ema_day 7 ema_day
6 ema_beep_f 6 ema_beep_f
Observations 5110 5110
Marginal R2 / Conditional R2 0.002 / NA NA

4.1.3 Phyisiology Stress

We also want to see if theres a general difference between the physiology variables and the weeks.To do this we build separate models for each physiology data feature. We also model the same covariates from before, but we also add to them temperature related changes, as we expect these to be highly singificant and related to our physiology. We present the results for the skin conductance and heart rate separately, and then together with FDR correction.

4.1.3.1 Skin Conductance

First we model the skin conductance, controlling for skin temparature. It looks like there is a big difference between the weeks, though not in the expected direction. For each model, we sekected the best family and link fit and present those below.

Tonic SC
# Model
glmer.sc_ton_mean_week <- glmer( sc_tonic_mean_s ~ Week_Type + 
    Sex + Program + # Model pop differences
    First_Week +  ema_beep_f*ema_day + # Model day related differencxes
    physical_excercise_dur + acc_delta + # Modle movement stuff
    temp_mean_z + temp_slope_z +  # Model temp effects
    (1+Week_Type |castor_record_id) + 
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id) + 
    (0+physical_excercise_dur|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (1 | castor_record_id:ema_day:ema_beep_f), 
    EMA_Pub, 
    family=Gamma(link="log"),
    control=lmerControl(calc.derivs = FALSE) )
please use glmerControl() instead of lmerControl()
# Model Summary
summary(glmer.sc_ton_mean_week)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( log )
Formula: sc_tonic_mean_s ~ Week_Type + Sex + Program + First_Week + ema_beep_f *      ema_day + physical_excercise_dur + acc_delta + temp_mean_z +  
    temp_slope_z + (1 + Week_Type | castor_record_id) + (0 +      temp_slope_z | castor_record_id) + (0 + temp_mean_z | castor_record_id) +  
    (0 + physical_excercise_dur | castor_record_id) + (0 + acc_delta |      castor_record_id) + (1 | castor_record_id:ema_day:ema_beep_f)
   Data: EMA_Pub
Control: lmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 -1405.7  -1022.7    761.8  -1523.7     4812 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.4589 -0.2899 -0.0689  0.1329  9.3566 

Random effects:
 Groups                              Name                   Variance Std.Dev. Corr 
 castor_record_id.ema_day.ema_beep_f (Intercept)            0.025340 0.159184      
 castor_record_id                    acc_delta              0.000078 0.008832      
 castor_record_id.1                  physical_excercise_dur 0.029822 0.172690      
 castor_record_id.2                  temp_mean_z            0.002067 0.045464      
 castor_record_id.3                  temp_slope_z           0.003169 0.056292      
 castor_record_id.4                  (Intercept)            0.003159 0.056208      
                                     Week_TypeStress        0.005701 0.075503 -0.85
 Residual                                                   0.031393 0.177182      
Number of obs: 4871, groups:  castor_record_id:ema_day:ema_beep_f, 2985; castor_record_id, 82

Fixed effects:
                            Estimate Std. Error t value Pr(>|z|)    
(Intercept)                0.1039732  0.0281128   3.698 0.000217 ***
Week_TypeStress           -0.0077766  0.0102403  -0.759 0.447605    
SexMale                    0.0005708  0.0129481   0.044 0.964836    
ProgramP2                 -0.0369714  0.0142713  -2.591 0.009581 ** 
First_WeekExam-First      -0.0375530  0.0132528  -2.834 0.004603 ** 
ema_beep_f2               -0.0120914  0.0356987  -0.339 0.734831    
ema_beep_f3                0.0177033  0.0352335   0.502 0.615346    
ema_beep_f4               -0.0142781  0.0354812  -0.402 0.687380    
ema_beep_f5               -0.0120938  0.0370798  -0.326 0.744307    
ema_beep_f6                0.0362003  0.0361193   1.002 0.316226    
ema_dayEMA 2.             -0.0060416  0.0357477  -0.169 0.865792    
ema_dayEMA 3.             -0.0625819  0.0361515  -1.731 0.083434 .  
ema_dayEMA 4.             -0.0193552  0.0361262  -0.536 0.592121    
ema_dayEMA 5.             -0.0644634  0.0360596  -1.788 0.073826 .  
ema_dayEMA 6.             -0.0405873  0.0369004  -1.100 0.271369    
ema_dayEMA 7.             -0.0486189  0.0368952  -1.318 0.187584    
physical_excercise_dur     0.0578554  0.0323015   1.791 0.073276 .  
acc_delta                  0.0125550  0.0012642   9.931  < 2e-16 ***
temp_mean_z                0.0213790  0.0067952   3.146 0.001654 ** 
temp_slope_z               0.0224963  0.0080180   2.806 0.005020 ** 
ema_beep_f2:ema_dayEMA 2. -0.0207045  0.0498834  -0.415 0.678100    
ema_beep_f3:ema_dayEMA 2.  0.0057906  0.0499772   0.116 0.907760    
ema_beep_f4:ema_dayEMA 2. -0.0123862  0.0501674  -0.247 0.804988    
ema_beep_f5:ema_dayEMA 2. -0.0476772  0.0511883  -0.931 0.351643    
ema_beep_f6:ema_dayEMA 2. -0.0553247  0.0506377  -1.093 0.274587    
ema_beep_f2:ema_dayEMA 3.  0.0204893  0.0506728   0.404 0.685959    
ema_beep_f3:ema_dayEMA 3. -0.0075935  0.0501722  -0.151 0.879700    
ema_beep_f4:ema_dayEMA 3.  0.0175097  0.0500830   0.350 0.726629    
ema_beep_f5:ema_dayEMA 3.  0.0454917  0.0519473   0.876 0.381178    
ema_beep_f6:ema_dayEMA 3.  0.0257633  0.0506955   0.508 0.611315    
ema_beep_f2:ema_dayEMA 4. -0.0257218  0.0508428  -0.506 0.612922    
ema_beep_f3:ema_dayEMA 4. -0.0753644  0.0503573  -1.497 0.134499    
ema_beep_f4:ema_dayEMA 4. -0.0352737  0.0503054  -0.701 0.483184    
ema_beep_f5:ema_dayEMA 4. -0.0134256  0.0515284  -0.261 0.794442    
ema_beep_f6:ema_dayEMA 4. -0.0661724  0.0506176  -1.307 0.191111    
ema_beep_f2:ema_dayEMA 5.  0.0286201  0.0503263   0.569 0.569566    
ema_beep_f3:ema_dayEMA 5.  0.0069213  0.0499645   0.139 0.889826    
ema_beep_f4:ema_dayEMA 5.  0.0094873  0.0503138   0.189 0.850437    
ema_beep_f5:ema_dayEMA 5. -0.0066590  0.0531778  -0.125 0.900349    
ema_beep_f6:ema_dayEMA 5. -0.0011590  0.0507614  -0.023 0.981784    
ema_beep_f2:ema_dayEMA 6.  0.0091557  0.0508887   0.180 0.857218    
ema_beep_f3:ema_dayEMA 6. -0.0236810  0.0506816  -0.467 0.640321    
ema_beep_f4:ema_dayEMA 6. -0.0165692  0.0512936  -0.323 0.746675    
ema_beep_f5:ema_dayEMA 6. -0.0050347  0.0532600  -0.095 0.924687    
ema_beep_f6:ema_dayEMA 6. -0.0412898  0.0521794  -0.791 0.428767    
ema_beep_f2:ema_dayEMA 7.  0.0142632  0.0518275   0.275 0.783159    
ema_beep_f3:ema_dayEMA 7. -0.0051180  0.0508239  -0.101 0.919788    
ema_beep_f4:ema_dayEMA 7.  0.0357892  0.0517982   0.691 0.489606    
ema_beep_f5:ema_dayEMA 7.  0.0174751  0.0527506   0.331 0.740435    
ema_beep_f6:ema_dayEMA 7. -0.0444276  0.0573065  -0.775 0.438185    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 50 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
Phasic Num
# Model
glmer.sc_ph_num <- glmer( sc_phasic_num ~  Week_Type + 
    Sex + Program + # Model pop differences
    First_Week +  ema_beep_f*ema_day + # Model day related differencxes
    physical_excercise_dur + acc_delta + # Modle movement stuff
    temp_mean_z + temp_slope_z +  # Model temp effects
    (1+Week_Type |castor_record_id) + 
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id) + 
    (0+physical_excercise_dur|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (1 | castor_record_id:ema_day:ema_beep_f),  
    EMA_Data, 
    family=poisson(link="log"),
    control=lmerControl(calc.derivs = FALSE) )
# Model Summary
summary(glmer.sc_ph_num)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: poisson  ( log )
Formula: sc_phasic_num ~ Week_Type + Sex + Program + First_Week + ema_beep_f *      ema_day + physical_excercise_dur + acc_delta + temp_mean_z +  
    temp_slope_z + (1 + Week_Type | castor_record_id) + (0 +      temp_slope_z | castor_record_id) + (0 + temp_mean_z | castor_record_id) +  
    (0 + physical_excercise_dur | castor_record_id) + (0 + acc_delta |      castor_record_id) + (1 | castor_record_id:ema_day:ema_beep_f)
   Data: EMA_Data
Control: lmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 47853.3  48229.8 -23868.6  47737.3     4813 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
  -6.35   -0.98   -0.13    0.61 2852.96 

Random effects:
 Groups                              Name                   Variance Std.Dev. Corr 
 castor_record_id.ema_day.ema_beep_f (Intercept)            1.55083  1.2453        
 castor_record_id                    acc_delta              0.01408  0.1187        
 castor_record_id.1                  physical_excercise_dur 7.07199  2.6593        
 castor_record_id.2                  temp_mean_z            0.35415  0.5951        
 castor_record_id.3                  temp_slope_z           0.22974  0.4793        
 castor_record_id.4                  (Intercept)            1.13258  1.0642        
                                     Week_TypeStress        0.48157  0.6940   -0.25
Number of obs: 4871, groups:  castor_record_id:ema_day:ema_beep_f, 2985; castor_record_id, 82

Fixed effects:
                           Estimate Std. Error z value Pr(>|z|)    
(Intercept)                1.523675   0.296412   5.140 2.74e-07 ***
Week_TypeStress           -0.277404   0.079256  -3.500 0.000465 ***
SexMale                    0.411508   0.245432   1.677 0.093607 .  
ProgramBSc_Med             0.131599   0.270989   0.486 0.627232    
First_WeekExam-First       0.035360   0.252223   0.140 0.888506    
ema_beep_f2               -0.011745   0.216371  -0.054 0.956711    
ema_beep_f3               -0.268295   0.213526  -1.256 0.208935    
ema_beep_f4               -0.456449   0.217091  -2.103 0.035503 *  
ema_beep_f5               -0.481962   0.225426  -2.138 0.032516 *  
ema_beep_f6               -0.318057   0.219996  -1.446 0.148250    
ema_dayEMA 2.             -0.110218   0.217110  -0.508 0.611691    
ema_dayEMA 3.             -0.547372   0.220549  -2.482 0.013070 *  
ema_dayEMA 4.             -0.580820   0.218951  -2.653 0.007984 ** 
ema_dayEMA 5.             -0.600885   0.219100  -2.743 0.006097 ** 
ema_dayEMA 6.             -0.437176   0.225205  -1.941 0.052230 .  
ema_dayEMA 7.             -0.500067   0.223759  -2.235 0.025427 *  
physical_excercise_dur     0.065567   0.321188   0.204 0.838246    
acc_delta                  0.145693   0.013506  10.787  < 2e-16 ***
temp_mean_z                0.315208   0.068331   4.613 3.97e-06 ***
temp_slope_z               0.192522   0.056122   3.430 0.000603 ***
ema_beep_f2:ema_dayEMA 2. -0.305653   0.304289  -1.004 0.315145    
ema_beep_f3:ema_dayEMA 2.  0.092300   0.303511   0.304 0.761045    
ema_beep_f4:ema_dayEMA 2.  0.244280   0.306453   0.797 0.425382    
ema_beep_f5:ema_dayEMA 2.  0.082331   0.312866   0.263 0.792435    
ema_beep_f6:ema_dayEMA 2. -0.575847   0.312028  -1.845 0.064965 .  
ema_beep_f2:ema_dayEMA 3.  0.200729   0.309550   0.648 0.516692    
ema_beep_f3:ema_dayEMA 3.  0.414335   0.306314   1.353 0.176168    
ema_beep_f4:ema_dayEMA 3.  0.466277   0.307134   1.518 0.128976    
ema_beep_f5:ema_dayEMA 3.  0.488258   0.317028   1.540 0.123533    
ema_beep_f6:ema_dayEMA 3.  0.303923   0.311133   0.977 0.328656    
ema_beep_f2:ema_dayEMA 4.  0.102194   0.310083   0.330 0.741724    
ema_beep_f3:ema_dayEMA 4.  0.216596   0.307691   0.704 0.481470    
ema_beep_f4:ema_dayEMA 4.  0.483253   0.308373   1.567 0.117090    
ema_beep_f5:ema_dayEMA 4.  0.444842   0.315535   1.410 0.158598    
ema_beep_f6:ema_dayEMA 4.  0.189572   0.311614   0.608 0.542951    
ema_beep_f2:ema_dayEMA 5. -0.106392   0.307793  -0.346 0.729597    
ema_beep_f3:ema_dayEMA 5.  0.324091   0.306169   1.059 0.289811    
ema_beep_f4:ema_dayEMA 5.  0.599767   0.307864   1.948 0.051396 .  
ema_beep_f5:ema_dayEMA 5.  0.096859   0.325250   0.298 0.765858    
ema_beep_f6:ema_dayEMA 5. -0.001503   0.313446  -0.005 0.996175    
ema_beep_f2:ema_dayEMA 6.  0.017425   0.311119   0.056 0.955337    
ema_beep_f3:ema_dayEMA 6.  0.244953   0.310796   0.788 0.430610    
ema_beep_f4:ema_dayEMA 6.  0.303635   0.314886   0.964 0.334911    
ema_beep_f5:ema_dayEMA 6.  0.190439   0.326884   0.583 0.560170    
ema_beep_f6:ema_dayEMA 6. -0.161854   0.322898  -0.501 0.616193    
ema_beep_f2:ema_dayEMA 7.  0.188897   0.314941   0.600 0.548650    
ema_beep_f3:ema_dayEMA 7.  0.254727   0.310815   0.820 0.412475    
ema_beep_f4:ema_dayEMA 7.  0.207454   0.318416   0.652 0.514711    
ema_beep_f5:ema_dayEMA 7. -0.024657   0.322544  -0.076 0.939064    
ema_beep_f6:ema_dayEMA 7.  0.110373   0.348213   0.317 0.751267    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 50 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
Phasic Magnitude
# Model
glmer.sc_ph_mag <- glmer( sc_phasic_mag_s ~ Week_Type + 
    Sex + Program + # Model pop differences
    First_Week +  ema_beep_f*ema_day + # Model day related differencxes
    physical_excercise_dur +acc_delta + # Modle movement stuff
    temp_mean_z + temp_slope_z +  # Model temp effects
    (1+Week_Type |castor_record_id) + 
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id) + 
    (0+physical_excercise_dur|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (1 | castor_record_id:ema_day:ema_beep_f), 
    EMA_Data, 
    family=Gamma(link="identity"),
    control=lmerControl(calc.derivs = FALSE) )
# Model Summary
summary(glmer.sc_ph_mag)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( identity )
Formula: sc_phasic_mag_s ~ Week_Type + Sex + Program + First_Week + ema_beep_f *      ema_day + physical_excercise_dur + acc_delta + temp_mean_z +  
    temp_slope_z + (1 + Week_Type | castor_record_id) + (0 +      temp_slope_z | castor_record_id) + (0 + temp_mean_z | castor_record_id) +  
    (0 + physical_excercise_dur | castor_record_id) + (0 + acc_delta |      castor_record_id) + (1 | castor_record_id:ema_day:ema_beep_f)
   Data: EMA_Data
Control: lmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 11102.2  11485.2  -5492.1  10984.2     4812 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.1393 -0.5111 -0.0753  0.4612  5.1547 

Random effects:
 Groups                              Name                   Variance Std.Dev. Corr 
 castor_record_id.ema_day.ema_beep_f (Intercept)            0.264007 0.51382       
 castor_record_id                    acc_delta              0.001006 0.03172       
 castor_record_id.1                  physical_excercise_dur 0.249678 0.49968       
 castor_record_id.2                  temp_mean_z            0.018295 0.13526       
 castor_record_id.3                  temp_slope_z           0.013368 0.11562       
 castor_record_id.4                  (Intercept)            0.071972 0.26828       
                                     Week_TypeStress        0.094414 0.30727  -0.70
 Residual                                                   0.115606 0.34001       
Number of obs: 4871, groups:  castor_record_id:ema_day:ema_beep_f, 2985; castor_record_id, 82

Fixed effects:
                           Estimate Std. Error t value Pr(>|z|)    
(Intercept)                2.093246   0.115226  18.166  < 2e-16 ***
Week_TypeStress           -0.072225   0.040948  -1.764 0.077760 .  
SexMale                    0.095661   0.059135   1.618 0.105736    
ProgramBSc_Med            -0.005529   0.065055  -0.085 0.932266    
First_WeekExam-First      -0.011885   0.060522  -0.196 0.844318    
ema_beep_f2               -0.060104   0.130928  -0.459 0.646193    
ema_beep_f3               -0.059550   0.129908  -0.458 0.646666    
ema_beep_f4               -0.110365   0.129911  -0.850 0.395579    
ema_beep_f5               -0.221627   0.133360  -1.662 0.096540 .  
ema_beep_f6               -0.023463   0.131712  -0.178 0.858614    
ema_dayEMA 2.             -0.111098   0.130270  -0.853 0.393752    
ema_dayEMA 3.             -0.206161   0.130914  -1.575 0.115305    
ema_dayEMA 4.             -0.127115   0.131401  -0.967 0.333352    
ema_dayEMA 5.             -0.190647   0.129539  -1.472 0.141095    
ema_dayEMA 6.             -0.177423   0.132971  -1.334 0.182105    
ema_dayEMA 7.             -0.094416   0.135203  -0.698 0.484971    
physical_excercise_dur     0.252229   0.109263   2.308 0.020973 *  
acc_delta                  0.102322   0.005050  20.263  < 2e-16 ***
temp_mean_z                0.081751   0.022762   3.592 0.000329 ***
temp_slope_z               0.071418   0.022305   3.202 0.001365 ** 
ema_beep_f2:ema_dayEMA 2.  0.067655   0.181341   0.373 0.709088    
ema_beep_f3:ema_dayEMA 2.  0.201175   0.184299   1.092 0.275023    
ema_beep_f4:ema_dayEMA 2.  0.070759   0.181796   0.389 0.697113    
ema_beep_f5:ema_dayEMA 2.  0.185545   0.183532   1.011 0.312033    
ema_beep_f6:ema_dayEMA 2. -0.093371   0.180503  -0.517 0.604959    
ema_beep_f2:ema_dayEMA 3.  0.081457   0.182670   0.446 0.655654    
ema_beep_f3:ema_dayEMA 3.  0.066165   0.181212   0.365 0.715018    
ema_beep_f4:ema_dayEMA 3.  0.143242   0.180705   0.793 0.427960    
ema_beep_f5:ema_dayEMA 3.  0.212893   0.184544   1.154 0.248658    
ema_beep_f6:ema_dayEMA 3.  0.184762   0.182242   1.014 0.310667    
ema_beep_f2:ema_dayEMA 4.  0.043410   0.183713   0.236 0.813207    
ema_beep_f3:ema_dayEMA 4.  0.031317   0.182296   0.172 0.863600    
ema_beep_f4:ema_dayEMA 4. -0.005062   0.180792  -0.028 0.977661    
ema_beep_f5:ema_dayEMA 4.  0.166133   0.183680   0.904 0.365746    
ema_beep_f6:ema_dayEMA 4. -0.107581   0.180147  -0.597 0.550384    
ema_beep_f2:ema_dayEMA 5. -0.010541   0.179333  -0.059 0.953130    
ema_beep_f3:ema_dayEMA 5.  0.049086   0.179319   0.274 0.784286    
ema_beep_f4:ema_dayEMA 5.  0.157847   0.181273   0.871 0.383882    
ema_beep_f5:ema_dayEMA 5.  0.187414   0.188383   0.995 0.319805    
ema_beep_f6:ema_dayEMA 5. -0.072172   0.179292  -0.403 0.687289    
ema_beep_f2:ema_dayEMA 6.  0.161451   0.184067   0.877 0.380416    
ema_beep_f3:ema_dayEMA 6.  0.078590   0.182438   0.431 0.666631    
ema_beep_f4:ema_dayEMA 6.  0.110882   0.183722   0.604 0.546153    
ema_beep_f5:ema_dayEMA 6.  0.239192   0.189040   1.265 0.205765    
ema_beep_f6:ema_dayEMA 6. -0.066544   0.183993  -0.362 0.717602    
ema_beep_f2:ema_dayEMA 7.  0.142784   0.189780   0.752 0.451833    
ema_beep_f3:ema_dayEMA 7. -0.020486   0.184394  -0.111 0.911538    
ema_beep_f4:ema_dayEMA 7.  0.023701   0.187879   0.126 0.899613    
ema_beep_f5:ema_dayEMA 7.  0.002820   0.187815   0.015 0.988021    
ema_beep_f6:ema_dayEMA 7. -0.037235   0.204576  -0.182 0.855574    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 50 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
Phasic AUC
# Model
glmer.sc_ph_auc_week <- glmer( sc_phasic_auc_s  ~ Week_Type + 
    Sex + Program + # Model pop differences
    First_Week +  ema_beep_f*ema_day + # Model day related differencxes
    physical_excercise_dur +acc_delta + # Modle movement stuff
    temp_mean_z + temp_slope_z +  # Model temp effects
    (1+Week_Type |castor_record_id) + 
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id) + 
    (0+physical_excercise_dur|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (1 | castor_record_id:ema_day:ema_beep_f), 
    EMA_Data, 
    family=Gamma(link=log),
    control=lmerControl(calc.derivs = FALSE) )
please use glmerControl() instead of lmerControl()
# Model Summary
summary(glmer.sc_ph_auc_week)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( log )
Formula: sc_phasic_auc_s ~ Week_Type + Sex + Program + First_Week + ema_beep_f *      ema_day + physical_excercise_dur + acc_delta + temp_mean_z +  
    temp_slope_z + (1 + Week_Type | castor_record_id) + (0 +      temp_slope_z | castor_record_id) + (0 + temp_mean_z | castor_record_id) +  
    (0 + physical_excercise_dur | castor_record_id) + (0 + acc_delta |      castor_record_id) + (1 | castor_record_id:ema_day:ema_beep_f)
   Data: EMA_Data
Control: lmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
  8774.4   9157.4  -4328.2   8656.4     4812 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.2859 -0.4668 -0.1553  0.2620  4.5998 

Random effects:
 Groups                              Name                   Variance  Std.Dev. Corr 
 castor_record_id.ema_day.ema_beep_f (Intercept)            0.0895855 0.29931       
 castor_record_id                    acc_delta              0.0002871 0.01694       
 castor_record_id.1                  physical_excercise_dur 0.0820159 0.28638       
 castor_record_id.2                  temp_mean_z            0.0080251 0.08958       
 castor_record_id.3                  temp_slope_z           0.0082019 0.09056       
 castor_record_id.4                  (Intercept)            0.0216869 0.14726       
                                     Week_TypeStress        0.0249042 0.15781  -0.64
 Residual                                                   0.1171402 0.34226       
Number of obs: 4871, groups:  castor_record_id:ema_day:ema_beep_f, 2985; castor_record_id, 82

Fixed effects:
                           Estimate Std. Error t value Pr(>|z|)    
(Intercept)                0.388492   0.061034   6.365 1.95e-10 ***
Week_TypeStress           -0.060887   0.020911  -2.912  0.00359 ** 
SexMale                    0.012285   0.033666   0.365  0.71518    
ProgramBSc_Med             0.014510   0.037136   0.391  0.69601    
First_WeekExam-First      -0.034996   0.034550  -1.013  0.31110    
ema_beep_f2               -0.060557   0.067910  -0.892  0.37254    
ema_beep_f3               -0.032083   0.067033  -0.479  0.63221    
ema_beep_f4               -0.157141   0.067499  -2.328  0.01991 *  
ema_beep_f5               -0.142661   0.070590  -2.021  0.04328 *  
ema_beep_f6               -0.014964   0.068758  -0.218  0.82772    
ema_dayEMA 2.             -0.020134   0.068014  -0.296  0.76721    
ema_dayEMA 3.             -0.175363   0.068832  -2.548  0.01084 *  
ema_dayEMA 4.             -0.180634   0.068761  -2.627  0.00861 ** 
ema_dayEMA 5.             -0.190408   0.068637  -2.774  0.00554 ** 
ema_dayEMA 6.             -0.174990   0.070238  -2.491  0.01273 *  
ema_dayEMA 7.             -0.150953   0.070240  -2.149  0.03163 *  
physical_excercise_dur     0.067279   0.058161   1.157  0.24737    
acc_delta                  0.038351   0.002432  15.771  < 2e-16 ***
temp_mean_z                0.065834   0.013469   4.888 1.02e-06 ***
temp_slope_z               0.044050   0.013787   3.195  0.00140 ** 
ema_beep_f2:ema_dayEMA 2. -0.014153   0.094906  -0.149  0.88145    
ema_beep_f3:ema_dayEMA 2. -0.023035   0.095075  -0.242  0.80856    
ema_beep_f4:ema_dayEMA 2.  0.038281   0.095443   0.401  0.68836    
ema_beep_f5:ema_dayEMA 2.  0.025079   0.097405   0.257  0.79681    
ema_beep_f6:ema_dayEMA 2. -0.179572   0.096357  -1.864  0.06238 .  
ema_beep_f2:ema_dayEMA 3.  0.109953   0.096395   1.141  0.25401    
ema_beep_f3:ema_dayEMA 3.  0.036368   0.095491   0.381  0.70331    
ema_beep_f4:ema_dayEMA 3.  0.172527   0.095298   1.810  0.07023 .  
ema_beep_f5:ema_dayEMA 3.  0.184727   0.098905   1.868  0.06180 .  
ema_beep_f6:ema_dayEMA 3.  0.112934   0.096504   1.170  0.24190    
ema_beep_f2:ema_dayEMA 4.  0.155081   0.096723   1.603  0.10886    
ema_beep_f3:ema_dayEMA 4.  0.051746   0.095831   0.540  0.58922    
ema_beep_f4:ema_dayEMA 4.  0.162519   0.095714   1.698  0.08951 .  
ema_beep_f5:ema_dayEMA 4.  0.155729   0.098066   1.588  0.11228    
ema_beep_f6:ema_dayEMA 4.  0.002540   0.096318   0.026  0.97896    
ema_beep_f2:ema_dayEMA 5.  0.071225   0.095751   0.744  0.45696    
ema_beep_f3:ema_dayEMA 5.  0.078734   0.095070   0.828  0.40758    
ema_beep_f4:ema_dayEMA 5.  0.217518   0.095739   2.272  0.02309 *  
ema_beep_f5:ema_dayEMA 5.  0.083740   0.101236   0.827  0.40814    
ema_beep_f6:ema_dayEMA 5.  0.055089   0.096615   0.570  0.56855    
ema_beep_f2:ema_dayEMA 6.  0.126453   0.096835   1.306  0.19160    
ema_beep_f3:ema_dayEMA 6.  0.079257   0.096455   0.822  0.41125    
ema_beep_f4:ema_dayEMA 6.  0.148516   0.097619   1.521  0.12816    
ema_beep_f5:ema_dayEMA 6.  0.122388   0.101392   1.207  0.22740    
ema_beep_f6:ema_dayEMA 6.  0.054131   0.099315   0.545  0.58572    
ema_beep_f2:ema_dayEMA 7.  0.099943   0.098605   1.014  0.31079    
ema_beep_f3:ema_dayEMA 7.  0.061271   0.096719   0.634  0.52641    
ema_beep_f4:ema_dayEMA 7.  0.141078   0.098593   1.431  0.15245    
ema_beep_f5:ema_dayEMA 7.  0.006557   0.100436   0.065  0.94795    
ema_beep_f6:ema_dayEMA 7.  0.031370   0.109115   0.287  0.77373    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 50 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
Table

Hear we can see that overall the measures seem to go down. We still need to correct for multiple comparrisons, but we can do this at the end when we also factor in our heart rate models to also include that informaiton in the FDR correction.

tab_model(glmer.sc_ton_mean_week, glmer.sc_ph_num, glmer.sc_ph_mag, glmer.sc_ph_auc_week, 
         terms=c("(Intercept)","Week_Type [Stress]", "Sex [Male]", "Program [BSc_Med]", "First_Week [Exam-First]", "acc_delta", "physical_excercise_dur"), 
          dv.labels=c("Tonic", "Number", "Magnitude", "AUC"), 
          title="Table 3. SC vs Week Type", 
          transform=NULL, 
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
Table 3. SC vs Week Type
  Tonic Number Magnitude AUC
Predictors Estimates std. Error CI Statistic p Log-Mean std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p
(Intercept) 0.10 0.03 0.05 – 0.16 3.70 <0.001 1.52 0.30 0.94 – 2.10 5.14 <0.001 2.09 0.12 1.87 – 2.32 18.17 <0.001 0.39 0.06 0.27 – 0.51 6.37 <0.001
Week_Type [Stress] -0.01 0.01 -0.03 – 0.01 -0.76 0.448 -0.28 0.08 -0.43 – -0.12 -3.50 <0.001 -0.07 0.04 -0.15 – 0.01 -1.76 0.078 -0.06 0.02 -0.10 – -0.02 -2.91 0.004
Sex [Male] 0.00 0.01 -0.02 – 0.03 0.04 0.965 0.41 0.25 -0.07 – 0.89 1.68 0.094 0.10 0.06 -0.02 – 0.21 1.62 0.106 0.01 0.03 -0.05 – 0.08 0.36 0.715
First_Week [Exam-First] -0.04 0.01 -0.06 – -0.01 -2.83 0.005 0.04 0.25 -0.46 – 0.53 0.14 0.889 -0.01 0.06 -0.13 – 0.11 -0.20 0.844 -0.03 0.03 -0.10 – 0.03 -1.01 0.311
physical_excercise_dur 0.06 0.03 -0.01 – 0.12 1.79 0.073 0.07 0.32 -0.56 – 0.70 0.20 0.838 0.25 0.11 0.04 – 0.47 2.31 0.021 0.07 0.06 -0.05 – 0.18 1.16 0.247
acc_delta 0.01 0.00 0.01 – 0.02 9.93 <0.001 0.15 0.01 0.12 – 0.17 10.79 <0.001 0.10 0.01 0.09 – 0.11 20.26 <0.001 0.04 0.00 0.03 – 0.04 15.77 <0.001
Program [BSc_Med] 0.13 0.27 -0.40 – 0.66 0.49 0.627 -0.01 0.07 -0.13 – 0.12 -0.08 0.932 0.01 0.04 -0.06 – 0.09 0.39 0.696
N 82 castor_record_id 82 castor_record_id 82 castor_record_id 82 castor_record_id
7 ema_day 7 ema_day 7 ema_day 7 ema_day
6 ema_beep_f 6 ema_beep_f 6 ema_beep_f 6 ema_beep_f
Observations 4871 4871 4871 4871

4.1.3.2 Heart Rate

We now take a look at the heart rate models. As the IBI data was way too sparse, it would be difficult to analyze the temporal domain changes. So we stick to simple measures of heart rate from the E4. Again, we fit the different families and links, and present the optimal fits below.

HR Mean
# Model
glmer.hr_mean_week <- glmer( hr_mean_s ~ Week_Type + 
    Sex + Program + # Model pop differences
    First_Week +  ema_beep_f*ema_day + # Model day related differencxes
    physical_excercise_dur +acc_delta + # Modle movement stuff
    temp_mean_z + temp_slope_z +  # Model temp effects
    (1+Week_Type |castor_record_id) + 
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id) + 
    (0+physical_excercise_dur|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (1 | castor_record_id:ema_day:ema_beep_f), 
    EMA_Data, 
    family=Gamma(link=identity),
    control=lmerControl(calc.derivs = FALSE) )
please use glmerControl() instead of lmerControl()
# Model Summary
summary(glmer.hr_mean_week)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( identity )
Formula: hr_mean_s ~ Week_Type + Sex + Program + First_Week + ema_beep_f *      ema_day + physical_excercise_dur + acc_delta + temp_mean_z +  
    temp_slope_z + (1 + Week_Type | castor_record_id) + (0 +      temp_slope_z | castor_record_id) + (0 + temp_mean_z | castor_record_id) +  
    (0 + physical_excercise_dur | castor_record_id) + (0 + acc_delta |      castor_record_id) + (1 | castor_record_id:ema_day:ema_beep_f)
   Data: EMA_Data
Control: lmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
  7540.8   7921.8  -3711.4   7422.8     4652 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.6174 -0.5158 -0.0471  0.4478  7.3365 

Random effects:
 Groups                              Name                   Variance  Std.Dev. Corr 
 castor_record_id.ema_day.ema_beep_f (Intercept)            0.1576115 0.39700       
 castor_record_id                    acc_delta              0.0009036 0.03006       
 castor_record_id.1                  physical_excercise_dur 0.1658048 0.40719       
 castor_record_id.2                  temp_mean_z            0.0239130 0.15464       
 castor_record_id.3                  temp_slope_z           0.0176056 0.13269       
 castor_record_id.4                  (Intercept)            0.0614173 0.24783       
                                     Week_TypeStress        0.0369784 0.19230  -0.52
 Residual                                                   0.0193458 0.13909       
Number of obs: 4711, groups:  castor_record_id:ema_day:ema_beep_f, 2958; castor_record_id, 82

Fixed effects:
                            Estimate Std. Error t value Pr(>|z|)    
(Intercept)                3.258e+00  9.176e-02  35.510  < 2e-16 ***
Week_TypeStress           -5.645e-02  2.683e-02  -2.104 0.035364 *  
SexMale                   -5.306e-02  5.801e-02  -0.915 0.360282    
ProgramBSc_Med             1.327e-01  6.325e-02   2.098 0.035921 *  
First_WeekExam-First       1.170e-01  5.926e-02   1.975 0.048290 *  
ema_beep_f2               -2.979e-02  9.489e-02  -0.314 0.753560    
ema_beep_f3               -2.552e-02  9.450e-02  -0.270 0.787094    
ema_beep_f4                6.431e-02  9.596e-02   0.670 0.502775    
ema_beep_f5                3.320e-03  1.001e-01   0.033 0.973547    
ema_beep_f6               -3.340e-01  9.290e-02  -3.595 0.000325 ***
ema_dayEMA 2.              1.572e-03  9.490e-02   0.017 0.986788    
ema_dayEMA 3.             -4.255e-02  9.763e-02  -0.436 0.662965    
ema_dayEMA 4.             -1.048e-02  9.726e-02  -0.108 0.914158    
ema_dayEMA 5.             -7.373e-02  9.492e-02  -0.777 0.437296    
ema_dayEMA 6.              2.035e-02  9.899e-02   0.206 0.837104    
ema_dayEMA 7.             -4.639e-02  9.896e-02  -0.469 0.639195    
physical_excercise_dur     5.028e-01  8.337e-02   6.031 1.63e-09 ***
acc_delta                  1.292e-01  4.386e-03  29.451  < 2e-16 ***
temp_mean_z               -4.341e-02  2.211e-02  -1.963 0.049646 *  
temp_slope_z               3.394e-02  2.118e-02   1.602 0.109098    
ema_beep_f2:ema_dayEMA 2.  7.520e-02  1.334e-01   0.564 0.573021    
ema_beep_f3:ema_dayEMA 2.  1.439e-02  1.343e-01   0.107 0.914687    
ema_beep_f4:ema_dayEMA 2.  6.156e-02  1.358e-01   0.453 0.650418    
ema_beep_f5:ema_dayEMA 2.  3.539e-03  1.366e-01   0.026 0.979333    
ema_beep_f6:ema_dayEMA 2.  3.856e-02  1.296e-01   0.298 0.766002    
ema_beep_f2:ema_dayEMA 3.  9.751e-02  1.365e-01   0.714 0.474998    
ema_beep_f3:ema_dayEMA 3.  9.660e-04  1.349e-01   0.007 0.994289    
ema_beep_f4:ema_dayEMA 3.  2.665e-02  1.366e-01   0.195 0.845391    
ema_beep_f5:ema_dayEMA 3. -1.713e-02  1.398e-01  -0.123 0.902448    
ema_beep_f6:ema_dayEMA 3.  1.730e-02  1.309e-01   0.132 0.894853    
ema_beep_f2:ema_dayEMA 4. -6.651e-03  1.367e-01  -0.049 0.961203    
ema_beep_f3:ema_dayEMA 4.  3.250e-02  1.361e-01   0.239 0.811212    
ema_beep_f4:ema_dayEMA 4. -5.490e-02  1.370e-01  -0.401 0.688535    
ema_beep_f5:ema_dayEMA 4.  1.869e-02  1.389e-01   0.135 0.893001    
ema_beep_f6:ema_dayEMA 4.  3.422e-02  1.311e-01   0.261 0.794093    
ema_beep_f2:ema_dayEMA 5.  8.250e-02  1.327e-01   0.622 0.534262    
ema_beep_f3:ema_dayEMA 5.  1.017e-01  1.339e-01   0.759 0.447569    
ema_beep_f4:ema_dayEMA 5. -2.056e-02  1.346e-01  -0.153 0.878602    
ema_beep_f5:ema_dayEMA 5.  1.397e-02  1.405e-01   0.099 0.920821    
ema_beep_f6:ema_dayEMA 5.  1.603e-02  1.294e-01   0.124 0.901389    
ema_beep_f2:ema_dayEMA 6.  8.107e-02  1.361e-01   0.596 0.551292    
ema_beep_f3:ema_dayEMA 6. -1.189e-02  1.358e-01  -0.088 0.930242    
ema_beep_f4:ema_dayEMA 6.  2.460e-03  1.386e-01   0.018 0.985844    
ema_beep_f5:ema_dayEMA 6. -1.650e-01  1.423e-01  -1.160 0.246061    
ema_beep_f6:ema_dayEMA 6. -1.297e-01  1.335e-01  -0.972 0.331285    
ema_beep_f2:ema_dayEMA 7.  5.110e-02  1.380e-01   0.370 0.711229    
ema_beep_f3:ema_dayEMA 7.  5.378e-02  1.363e-01   0.395 0.693200    
ema_beep_f4:ema_dayEMA 7.  9.676e-05  1.407e-01   0.001 0.999451    
ema_beep_f5:ema_dayEMA 7.  5.961e-02  1.411e-01   0.422 0.672675    
ema_beep_f6:ema_dayEMA 7.  2.207e-01  1.478e-01   1.494 0.135247    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 50 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
HR Max
# Model
glmer.hr_max_week <- glmer( hr_max_s  ~ Week_Type + 
    Sex + Program + # Model pop differences
    First_Week +  ema_beep_f*ema_day + # Model day related differencxes
    physical_excercise_dur +acc_delta + # Modle movement stuff
    temp_mean_z + temp_slope_z +  # Model temp effects
    (1+Week_Type |castor_record_id) + 
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id) + 
    (0+physical_excercise_dur|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (1 | castor_record_id:ema_day:ema_beep_f),  
    EMA_Data, 
    family=Gamma(link="identity"),
    control=lmerControl(calc.derivs = FALSE) )
please use glmerControl() instead of lmerControl()
# Model SUmmary
summary(glmer.hr_max_week)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( identity )
Formula: hr_max_s ~ Week_Type + Sex + Program + First_Week + ema_beep_f *      ema_day + physical_excercise_dur + acc_delta + temp_mean_z +  
    temp_slope_z + (1 + Week_Type | castor_record_id) + (0 +      temp_slope_z | castor_record_id) + (0 + temp_mean_z | castor_record_id) +  
    (0 + physical_excercise_dur | castor_record_id) + (0 + acc_delta |      castor_record_id) + (1 | castor_record_id:ema_day:ema_beep_f)
   Data: EMA_Data
Control: lmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 11059.0  11440.0  -5470.5  10941.0     4652 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.5142 -0.5339 -0.0941  0.4672  5.3176 

Random effects:
 Groups                              Name                   Variance Std.Dev. Corr 
 castor_record_id.ema_day.ema_beep_f (Intercept)            0.321320 0.56685       
 castor_record_id                    acc_delta              0.001173 0.03425       
 castor_record_id.1                  physical_excercise_dur 0.265895 0.51565       
 castor_record_id.2                  temp_mean_z            0.031866 0.17851       
 castor_record_id.3                  temp_slope_z           0.020873 0.14447       
 castor_record_id.4                  (Intercept)            0.056195 0.23705       
                                     Week_TypeStress        0.041653 0.20409  -0.65
 Residual                                                   0.032039 0.17900       
Number of obs: 4711, groups:  castor_record_id:ema_day:ema_beep_f, 2958; castor_record_id, 82

Fixed effects:
                           Estimate Std. Error t value Pr(>|z|)    
(Intercept)                3.610979   0.117646  30.694  < 2e-16 ***
Week_TypeStress           -0.102658   0.032271  -3.181 0.001467 ** 
SexMale                    0.089559   0.059713   1.500 0.133663    
ProgramBSc_Med             0.070230   0.064731   1.085 0.277942    
First_WeekExam-First       0.111305   0.060799   1.831 0.067143 .  
ema_beep_f2               -0.074871   0.136659  -0.548 0.583782    
ema_beep_f3               -0.078602   0.136110  -0.577 0.563609    
ema_beep_f4                0.037330   0.138516   0.269 0.787547    
ema_beep_f5               -0.021750   0.144295  -0.151 0.880187    
ema_beep_f6               -0.460252   0.132760  -3.467 0.000527 ***
ema_dayEMA 2.             -0.068711   0.136734  -0.503 0.615302    
ema_dayEMA 3.             -0.132848   0.140371  -0.946 0.343939    
ema_dayEMA 4.              0.004396   0.140826   0.031 0.975100    
ema_dayEMA 5.             -0.284643   0.135693  -2.098 0.035932 *  
ema_dayEMA 6.             -0.006776   0.142700  -0.047 0.962129    
ema_dayEMA 7.             -0.004806   0.143771  -0.033 0.973334    
physical_excercise_dur     0.427944   0.113795   3.761 0.000169 ***
acc_delta                  0.159653   0.005583  28.598  < 2e-16 ***
temp_mean_z               -0.174829   0.027468  -6.365 1.95e-10 ***
temp_slope_z               0.027687   0.026663   1.038 0.299092    
ema_beep_f2:ema_dayEMA 2.  0.174511   0.192231   0.908 0.363973    
ema_beep_f3:ema_dayEMA 2.  0.141258   0.193521   0.730 0.465429    
ema_beep_f4:ema_dayEMA 2.  0.016042   0.195262   0.082 0.934524    
ema_beep_f5:ema_dayEMA 2.  0.097199   0.196780   0.494 0.621342    
ema_beep_f6:ema_dayEMA 2.  0.224705   0.185588   1.211 0.225983    
ema_beep_f2:ema_dayEMA 3.  0.186199   0.196239   0.949 0.342704    
ema_beep_f3:ema_dayEMA 3.  0.096146   0.193869   0.496 0.619941    
ema_beep_f4:ema_dayEMA 3.  0.133786   0.196860   0.680 0.496759    
ema_beep_f5:ema_dayEMA 3.  0.042645   0.200721   0.212 0.831750    
ema_beep_f6:ema_dayEMA 3.  0.236219   0.187347   1.261 0.207359    
ema_beep_f2:ema_dayEMA 4. -0.022167   0.197253  -0.112 0.910522    
ema_beep_f3:ema_dayEMA 4.  0.056756   0.196593   0.289 0.772813    
ema_beep_f4:ema_dayEMA 4. -0.149687   0.197554  -0.758 0.448628    
ema_beep_f5:ema_dayEMA 4. -0.056416   0.200066  -0.282 0.777953    
ema_beep_f6:ema_dayEMA 4.  0.148919   0.188120   0.792 0.428586    
ema_beep_f2:ema_dayEMA 5.  0.281035   0.190467   1.476 0.140076    
ema_beep_f3:ema_dayEMA 5.  0.319475   0.192048   1.664 0.096210 .  
ema_beep_f4:ema_dayEMA 5.  0.106318   0.192755   0.552 0.581243    
ema_beep_f5:ema_dayEMA 5.  0.161619   0.201315   0.803 0.422083    
ema_beep_f6:ema_dayEMA 5.  0.269338   0.183977   1.464 0.143200    
ema_beep_f2:ema_dayEMA 6.  0.038573   0.195616   0.197 0.843683    
ema_beep_f3:ema_dayEMA 6.  0.058879   0.195879   0.301 0.763729    
ema_beep_f4:ema_dayEMA 6. -0.036330   0.199439  -0.182 0.855456    
ema_beep_f5:ema_dayEMA 6. -0.209064   0.204663  -1.022 0.307017    
ema_beep_f6:ema_dayEMA 6.  0.044939   0.191264   0.235 0.814240    
ema_beep_f2:ema_dayEMA 7.  0.043551   0.200070   0.218 0.827681    
ema_beep_f3:ema_dayEMA 7.  0.115001   0.197599   0.582 0.560572    
ema_beep_f4:ema_dayEMA 7. -0.122129   0.203205  -0.601 0.547830    
ema_beep_f5:ema_dayEMA 7. -0.084735   0.203495  -0.416 0.677118    
ema_beep_f6:ema_dayEMA 7.  0.342276   0.212607   1.610 0.107420    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 50 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
HR Min
# Model
glmer.hr_min_week <- glmer( hr_min_s  ~ Week_Type + 
    Sex + Program + # Model pop differences
    First_Week +  ema_beep_f*ema_day + # Model day related differencxes
    physical_excercise_dur +acc_delta + # Modle movement stuff
    temp_mean_z + temp_slope_z +  # Model temp effects
    (1+Week_Type |castor_record_id) + 
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id) + 
    (0+physical_excercise_dur|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (1 | castor_record_id:ema_day:ema_beep_f), 
    EMA_Data, 
    family=Gamma(link="identity"),
    control=lmerControl(calc.derivs = FALSE) )
please use glmerControl() instead of lmerControl()
# Model Summary
summary(glmer.hr_min_week)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( identity )
Formula: hr_min_s ~ Week_Type + Sex + Program + First_Week + ema_beep_f *      ema_day + physical_excercise_dur + acc_delta + temp_mean_z +  
    temp_slope_z + (1 + Week_Type | castor_record_id) + (0 +      temp_slope_z | castor_record_id) + (0 + temp_mean_z | castor_record_id) +  
    (0 + physical_excercise_dur | castor_record_id) + (0 + acc_delta |      castor_record_id) + (1 | castor_record_id:ema_day:ema_beep_f)
   Data: EMA_Data
Control: lmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
  9628.6  10009.6  -4755.3   9510.6     4652 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.1208 -0.5161 -0.0216  0.4919  6.4178 

Random effects:
 Groups                              Name                   Variance  Std.Dev. Corr 
 castor_record_id.ema_day.ema_beep_f (Intercept)            0.2552349 0.50521       
 castor_record_id                    acc_delta              0.0006928 0.02632       
 castor_record_id.1                  physical_excercise_dur 0.2348128 0.48457       
 castor_record_id.2                  temp_mean_z            0.0245331 0.15663       
 castor_record_id.3                  temp_slope_z           0.0264318 0.16258       
 castor_record_id.4                  (Intercept)            0.0859233 0.29313       
                                     Week_TypeStress        0.0589009 0.24270  -0.42
 Residual                                                   0.0280606 0.16751       
Number of obs: 4711, groups:  castor_record_id:ema_day:ema_beep_f, 2958; castor_record_id, 82

Fixed effects:
                           Estimate Std. Error t value Pr(>|z|)    
(Intercept)                3.809929   0.113571  33.547  < 2e-16 ***
Week_TypeStress           -0.024566   0.033728  -0.728  0.46638    
SexMale                   -0.330923   0.071350  -4.638 3.52e-06 ***
ProgramBSc_Med             0.035281   0.077996   0.452  0.65103    
First_WeekExam-First       0.088413   0.073143   1.209  0.22675    
ema_beep_f2               -0.057447   0.119076  -0.482  0.62949    
ema_beep_f3               -0.062725   0.118461  -0.529  0.59646    
ema_beep_f4                0.122668   0.120279   1.020  0.30779    
ema_beep_f5               -0.029771   0.125545  -0.237  0.81255    
ema_beep_f6               -0.286848   0.117785  -2.435  0.01488 *  
ema_dayEMA 2.             -0.036492   0.118655  -0.308  0.75843    
ema_dayEMA 3.             -0.038427   0.122204  -0.314  0.75318    
ema_dayEMA 4.             -0.129207   0.120995  -1.068  0.28558    
ema_dayEMA 5.             -0.015433   0.119295  -0.129  0.89707    
ema_dayEMA 6.              0.091826   0.124785   0.736  0.46181    
ema_dayEMA 7.             -0.168629   0.122494  -1.377  0.16863    
physical_excercise_dur     0.535729   0.101994   5.253 1.50e-07 ***
acc_delta                  0.090369   0.004400  20.541  < 2e-16 ***
temp_mean_z                0.076989   0.024356   3.161  0.00157 ** 
temp_slope_z               0.038310   0.025882   1.480  0.13882    
ema_beep_f2:ema_dayEMA 2.  0.105223   0.167068   0.630  0.52881    
ema_beep_f3:ema_dayEMA 2.  0.034657   0.167848   0.206  0.83642    
ema_beep_f4:ema_dayEMA 2.  0.057317   0.170240   0.337  0.73636    
ema_beep_f5:ema_dayEMA 2.  0.031300   0.171108   0.183  0.85485    
ema_beep_f6:ema_dayEMA 2.  0.045726   0.164290   0.278  0.78076    
ema_beep_f2:ema_dayEMA 3.  0.081462   0.171153   0.476  0.63410    
ema_beep_f3:ema_dayEMA 3.  0.002299   0.169145   0.014  0.98915    
ema_beep_f4:ema_dayEMA 3. -0.054146   0.171183  -0.316  0.75177    
ema_beep_f5:ema_dayEMA 3.  0.048431   0.175802   0.275  0.78294    
ema_beep_f6:ema_dayEMA 3. -0.026465   0.165922  -0.160  0.87327    
ema_beep_f2:ema_dayEMA 4.  0.077673   0.170613   0.455  0.64892    
ema_beep_f3:ema_dayEMA 4.  0.052666   0.169281   0.311  0.75571    
ema_beep_f4:ema_dayEMA 4.  0.037419   0.171221   0.219  0.82701    
ema_beep_f5:ema_dayEMA 4.  0.252003   0.174334   1.446  0.14831    
ema_beep_f6:ema_dayEMA 4.  0.126668   0.165737   0.764  0.44471    
ema_beep_f2:ema_dayEMA 5.  0.001942   0.166537   0.012  0.99070    
ema_beep_f3:ema_dayEMA 5.  0.020570   0.167875   0.123  0.90248    
ema_beep_f4:ema_dayEMA 5. -0.167078   0.169147  -0.988  0.32327    
ema_beep_f5:ema_dayEMA 5. -0.010888   0.176530  -0.062  0.95082    
ema_beep_f6:ema_dayEMA 5. -0.045625   0.164892  -0.277  0.78201    
ema_beep_f2:ema_dayEMA 6.  0.037415   0.171167   0.219  0.82697    
ema_beep_f3:ema_dayEMA 6. -0.035933   0.170648  -0.211  0.83322    
ema_beep_f4:ema_dayEMA 6. -0.173388   0.174050  -0.996  0.31916    
ema_beep_f5:ema_dayEMA 6. -0.190617   0.179189  -1.064  0.28743    
ema_beep_f6:ema_dayEMA 6. -0.229110   0.170065  -1.347  0.17792    
ema_beep_f2:ema_dayEMA 7.  0.175024   0.171736   1.019  0.30813    
ema_beep_f3:ema_dayEMA 7.  0.154267   0.169720   0.909  0.36338    
ema_beep_f4:ema_dayEMA 7.  0.045564   0.175439   0.260  0.79509    
ema_beep_f5:ema_dayEMA 7.  0.121611   0.175545   0.693  0.48846    
ema_beep_f6:ema_dayEMA 7.  0.377271   0.186892   2.019  0.04352 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 50 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
Table
tab_model(glmer.hr_mean_week, glmer.hr_min_week, glmer.hr_max_week, glmer.hr_sd_week, 
          terms=c("(Intercept)","Week_Type [Stress]", "Sex [Male]", "Program [BSc_Med]", "First_Week [Exam-First]", "acc_delta", "physical_excercise_dur"), 
          dv.labels=c("Mean", "Min", "Max", "SD"), 
          title="Table 3. HR vs Week Type", #p.adjust = "fdr",
          transform=NULL, 
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
Table 3. HR vs Week Type
  Mean Min Max SD
Predictors Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p
(Intercept) 3.26 0.09 3.08 – 3.44 35.51 <0.001 3.81 0.11 3.59 – 4.03 33.55 <0.001 3.61 0.12 3.38 – 3.84 30.69 <0.001 0.80 0.05 0.70 – 0.89 16.52 <0.001
Week_Type [Stress] -0.06 0.03 -0.11 – -0.00 -2.10 0.035 -0.02 0.03 -0.09 – 0.04 -0.73 0.466 -0.10 0.03 -0.17 – -0.04 -3.18 0.001 -0.02 0.01 -0.05 – 0.00 -1.63 0.102
Sex [Male] -0.05 0.06 -0.17 – 0.06 -0.91 0.360 -0.33 0.07 -0.47 – -0.19 -4.64 <0.001 0.09 0.06 -0.03 – 0.21 1.50 0.134 0.13 0.03 0.08 – 0.18 5.13 <0.001
Program [BSc_Med] 0.13 0.06 0.01 – 0.26 2.10 0.036 0.04 0.08 -0.12 – 0.19 0.45 0.651 0.07 0.06 -0.06 – 0.20 1.08 0.278 0.01 0.03 -0.04 – 0.07 0.48 0.628
First_Week [Exam-First] 0.12 0.06 0.00 – 0.23 1.97 0.048 0.09 0.07 -0.05 – 0.23 1.21 0.227 0.11 0.06 -0.01 – 0.23 1.83 0.067 0.04 0.03 -0.01 – 0.09 1.54 0.123
physical_excercise_dur 0.50 0.08 0.34 – 0.67 6.03 <0.001 0.54 0.10 0.34 – 0.74 5.25 <0.001 0.43 0.11 0.20 – 0.65 3.76 <0.001 0.03 0.05 -0.07 – 0.13 0.62 0.533
acc_delta 0.13 0.00 0.12 – 0.14 29.45 <0.001 0.09 0.00 0.08 – 0.10 20.54 <0.001 0.16 0.01 0.15 – 0.17 28.60 <0.001 0.04 0.00 0.04 – 0.04 21.16 <0.001
N 82 castor_record_id 82 castor_record_id 82 castor_record_id 82 castor_record_id
7 ema_day 7 ema_day 7 ema_day 7 ema_day
6 ema_beep_f 6 ema_beep_f 6 ema_beep_f 6 ema_beep_f
Observations 4711 4711 4711 4711

4.1.3.3 Table and Plot: Physiology vs Weektype

I will now make a table for all physiology measures.These tables will also have the FDR adjusted values that we report in our article.

tab_model(glmer.sc_ton_mean_week, glmer.sc_ph_num, glmer.sc_ph_mag, glmer.sc_ph_auc_week, glmer.hr_mean_week, glmer.hr_min_week, glmer.hr_max_week, 
         terms=c("(Intercept)","Week_Type [Stress]", "Sex [Male]", "Program [BSc_Med]", "First_Week [Exam-First]", "acc_delta", "physical_excercise_dur", 
         "temp_mean_z", "temp_slope_z"), 
          dv.labels=c("SC Tonic", "SC Number", "SC Magnitude", "SC AUC", "HR Mean", "HR Min", "HR Max"), 
          title="Table 3. Physio vs Week Type", 
          transform=NULL, p.adjust="fdr",
         show.stat=TRUE,
         show.se=T) %>%  
    return() %$%
    knitr %>%
    asis_output()
Table 3. Physio vs Week Type
  SC Tonic SC Number SC Magnitude SC AUC HR Mean HR Min HR Max
Predictors Estimates std. Error CI Statistic p Log-Mean std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p
(Intercept) 0.10 0.03 0.05 – 0.16 3.70 0.005 1.52 0.30 0.94 – 2.10 5.14 <0.001 2.09 0.12 1.87 – 2.32 18.17 <0.001 0.39 0.06 0.27 – 0.51 6.37 <0.001 3.26 0.09 3.08 – 3.44 35.51 <0.001 3.81 0.11 3.59 – 4.03 33.55 <0.001 3.61 0.12 3.38 – 3.84 30.69 <0.001
Week_Type [Stress] -0.01 0.01 -0.03 – 0.01 -0.76 0.963 -0.28 0.08 -0.43 – -0.12 -3.50 0.006 -0.07 0.04 -0.15 – 0.01 -1.76 0.641 -0.06 0.02 -0.10 – -0.02 -2.91 0.036 -0.06 0.03 -0.11 – -0.00 -2.10 0.299 -0.02 0.03 -0.09 – 0.04 -0.73 0.960 -0.10 0.03 -0.17 – -0.04 -3.18 0.012
Sex [Male] 0.00 0.01 -0.02 – 0.03 0.04 0.982 0.41 0.25 -0.07 – 0.89 1.68 0.312 0.10 0.06 -0.02 – 0.21 1.62 0.641 0.01 0.03 -0.05 – 0.08 0.36 0.851 -0.05 0.06 -0.17 – 0.06 -0.91 0.999 -0.33 0.07 -0.47 – -0.19 -4.64 <0.001 0.09 0.06 -0.03 – 0.21 1.50 0.551
First_Week [Exam-First] -0.04 0.01 -0.06 – -0.01 -2.83 0.050 0.04 0.25 -0.46 – 0.53 0.14 0.966 -0.01 0.06 -0.13 – 0.11 -0.20 0.981 -0.03 0.03 -0.10 – 0.03 -1.01 0.556 0.12 0.06 0.00 – 0.23 1.97 0.310 0.09 0.07 -0.05 – 0.23 1.21 0.898 0.11 0.06 -0.01 – 0.23 1.83 0.420
physical_excercise_dur 0.06 0.03 -0.01 – 0.12 1.79 0.461 0.07 0.32 -0.56 – 0.70 0.20 0.931 0.25 0.11 0.04 – 0.47 2.31 0.210 0.07 0.06 -0.05 – 0.18 1.16 0.488 0.50 0.08 0.34 – 0.67 6.03 <0.001 0.54 0.10 0.34 – 0.74 5.25 <0.001 0.43 0.11 0.20 – 0.65 3.76 0.002
acc_delta 0.01 0.00 0.01 – 0.02 9.93 <0.001 0.15 0.01 0.12 – 0.17 10.79 <0.001 0.10 0.01 0.09 – 0.11 20.26 <0.001 0.04 0.00 0.03 – 0.04 15.77 <0.001 0.13 0.00 0.12 – 0.14 29.45 <0.001 0.09 0.00 0.08 – 0.10 20.54 <0.001 0.16 0.01 0.15 – 0.17 28.60 <0.001
temp_mean_z 0.02 0.01 0.01 – 0.03 3.15 0.028 0.32 0.07 0.18 – 0.45 4.61 <0.001 0.08 0.02 0.04 – 0.13 3.59 0.005 0.07 0.01 0.04 – 0.09 4.89 <0.001 -0.04 0.02 -0.09 – -0.00 -1.96 0.310 0.08 0.02 0.03 – 0.12 3.16 0.016 -0.17 0.03 -0.23 – -0.12 -6.36 <0.001
temp_slope_z 0.02 0.01 0.01 – 0.04 2.81 0.050 0.19 0.06 0.08 – 0.30 3.43 0.006 0.07 0.02 0.03 – 0.12 3.20 0.017 0.04 0.01 0.02 – 0.07 3.20 0.017 0.03 0.02 -0.01 – 0.08 1.60 0.606 0.04 0.03 -0.01 – 0.09 1.48 0.809 0.03 0.03 -0.02 – 0.08 1.04 0.853
Program [BSc_Med] 0.13 0.27 -0.40 – 0.66 0.49 0.825 -0.01 0.07 -0.13 – 0.12 -0.08 0.988 0.01 0.04 -0.06 – 0.09 0.39 0.851 0.13 0.06 0.01 – 0.26 2.10 0.299 0.04 0.08 -0.12 – 0.19 0.45 0.960 0.07 0.06 -0.06 – 0.20 1.08 0.853
N 82 castor_record_id 82 castor_record_id 82 castor_record_id 82 castor_record_id 82 castor_record_id 82 castor_record_id 82 castor_record_id
7 ema_day 7 ema_day 7 ema_day 7 ema_day 7 ema_day 7 ema_day 7 ema_day
6 ema_beep_f 6 ema_beep_f 6 ema_beep_f 6 ema_beep_f 6 ema_beep_f 6 ema_beep_f 6 ema_beep_f
Observations 4871 4871 4871 4871 4711 4711 4711

4.1.4 Plot: Outcome Measures

And now I also plot the figure we use in the article with all the outcome measures including the affect items. I again do FDR correction here.

# Together
plot.physio <- plot_models(glmer.posmood_week, glmer.sc_ton_mean_week, glmer.sc_ph_num)
rm_term <- as.vector(plot.physio$data$term[1:97])
rm_term <- rm_term[rm_term != "Week_TypeStress"]
# Color list
col_list <-c('#7570B3','#7570B3','#7570B3',"#D95F02", "#D95F02", '#D95F02', '#D95F02', "#1B9E77", "#1B9E77")
# Make the plot
plot.all_week_resid <- plot_models( glmer.posmood_week, glmer.negmood_week, 
            glmer.sc_ton_mean_week, glmer.sc_ph_num, glmer.sc_ph_mag, glmer.sc_ph_auc_week, 
            glmer.hr_mean_week, glmer.hr_min_week, glmer.hr_max_week,
            m.labels=c("Positive Affect", "Negative Affect", "SC Tonic", "SC Number", "SC Magnitued", "SC AUC","HR Mean", "HR Minimum", "HR Maximum"),
            axis.labels = c(" "),
            # Stastistical Stuff
            rm.terms = rm_term,
            #show.values = T,
            #value.size = 4, 
            #std.est=T, 
            show.p=T,
            p.shape=T,
            p.adjust = "fdr", 
            legend.pval.title = "Significance", 
            # Visual Stuff
            colors=col_list,
            dot.size=2,
            line.size = 1,
            spacing=0.7, 
            vline.color = "darkgrey", 
            legend.title = "") + 
            ptheme + 
            theme(axis.ticks.y=element_blank(), 
                  legend.text=element_text(size=16), legend.title = element_text(size=16),
                  axis.title = element_text(size=16),axis.text.x=element_text(size=11),
                  panel.grid.major.x = element_line(colour = "grey95"),
                  panel.grid.minor.x = element_line(colour = "grey90")) 
# Plot and save
plot.all_week_resid + coord_flip(ylim=c(-0.5,0.5)) + theme(panel.grid.major.y = element_line(colour = "grey95"), panel.grid.minor.y = element_line(colour = "grey90"))
Coordinate system already present. Adding new coordinate system, which will replace the existing one.

#ggsave("figures/fig_WeekResid_ALL.tiff", units="in", width=4, height=4, dpi=300, compression = 'lzw', bg="transparent")

So overall all, our first analysis confirms that our stress week results in increased stress. This has a direct consequence on mood outcomes, and physiology. But the physiology is not really in the expected direction which is a bit strange. Interestingly though, the physiology is in the same direction as positive affect. So this indicated to me maybe that we are looking at reductions in positive arousal.

4.2 Momentary Associations

Now we found week differences in both the EMA and EPA measures, the next step will be to investigate the relaitonship between subjective stress as and our outcome measures on a beep to beep level. This is a bit of a replicaiton attempt of previous studies, where we also try to explain the previous findings. Is it linked to positive affect as well?

For these models, we know that activity stress is correlated with event and social stress, which we present below. So to adjust for that, we also model interaction terms for these variables specifically. We model similar covariates, but not day here, only time of day since we arent looking at the weeks in a linear fashion. Due to convergence issues with the maximal models, we have a fixed intercept for our fixed effects of interest in these models.

Correlation Matrix

 rcorr(as.matrix(EMA_Data[,c("event_tot_s", "activity_tot_s", "social_tot_s", "physical_tot_s")]))
               event_tot_s activity_tot_s social_tot_s physical_tot_s
event_tot_s           1.00           0.42         0.17           0.07
activity_tot_s        0.42           1.00         0.34           0.15
social_tot_s          0.17           0.34         1.00           0.18
physical_tot_s        0.07           0.15         0.18           1.00

n
               event_tot_s activity_tot_s social_tot_s physical_tot_s
event_tot_s           6160           6153         6160           6146
activity_tot_s        6153           6153         6153           6146
social_tot_s          6160           6153         6623           6146
physical_tot_s        6146           6146         6146           6146

P
               event_tot_s activity_tot_s social_tot_s physical_tot_s
event_tot_s                 0              0            0            
activity_tot_s  0                          0            0            
social_tot_s    0           0                           0            
physical_tot_s  0           0              0                         

4.2.1 Mood

First we take a look at the affect/mood items.We use the maximal fitting with all the families and links, and pick the best fit for our results.

Positive

glmer.posmood_beep <- glmer(mood_positive_s ~ 
    event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=gaussian(link="identity"),
    control=lmerControl(calc.derivs = FALSE) )
please use glmerControl() instead of lmerControl()calling glmer() with family=gaussian (identity link) as a shortcut to lmer() is deprecated; please call lmer() directly
# Summary
summary(glmer.posmood_beep )
Linear mixed model fit by REML ['lmerMod']
Formula: mood_positive_s ~ event_tot_s * activity_tot_s + activity_tot_s *      social_tot_s + physical_tot_s + ema_beep + Sex + physical_excercise_dur +  
    acc_delta + temp_mean_z + temp_slope_z + (0 + event_tot_s +      activity_tot_s + social_tot_s + physical_tot_s | castor_record_id) +  
    (0 + ema_beep | castor_record_id) + (0 + temp_slope_z | castor_record_id) +  
    (0 + temp_mean_z | castor_record_id) + (0 + acc_delta | castor_record_id) +      (0 + physical_excercise_dur | castor_record_id)
   Data: EMA_Data
Control: lmerControl(calc.derivs = FALSE)

REML criterion at convergence: 15728.4

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-6.0466 -0.5682  0.0480  0.6304  3.7752 

Random effects:
 Groups             Name                   Variance Std.Dev. Corr             
 castor_record_id   event_tot_s            0.016084 0.12682                   
                    activity_tot_s         0.005431 0.07369  -0.23            
                    social_tot_s           0.012216 0.11053  -0.30  0.18      
                    physical_tot_s         0.017675 0.13295  -0.16 -0.45 -0.15
 castor_record_id.1 ema_beep               0.004990 0.07064                   
 castor_record_id.2 temp_slope_z           0.000000 0.00000                   
 castor_record_id.3 temp_mean_z            0.017711 0.13308                   
 castor_record_id.4 acc_delta              0.000000 0.00000                   
 castor_record_id.5 physical_excercise_dur 0.220847 0.46994                   
 Residual                                  1.120788 1.05867                   
Number of obs: 5109, groups:  castor_record_id, 82

Fixed effects:
                             Estimate Std. Error t value
(Intercept)                  9.735980   0.198727  48.992
event_tot_s                 -0.125210   0.033495  -3.738
activity_tot_s              -0.201643   0.039304  -5.130
social_tot_s                -0.295075   0.030157  -9.785
physical_tot_s              -0.152168   0.019395  -7.846
ema_beep                    -0.011329   0.012413  -0.913
SexMale                      0.262580   0.139864   1.877
physical_excercise_dur       0.566937   0.122851   4.615
acc_delta                    0.004665   0.003012   1.549
temp_mean_z                 -0.002554   0.025937  -0.098
temp_slope_z                -0.012033   0.015551  -0.774
event_tot_s:activity_tot_s  -0.016230   0.005886  -2.757
activity_tot_s:social_tot_s  0.025817   0.005103   5.059

Correlation matrix not shown by default, as p = 13 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it

Negative

glmer.negmood_beep <- glmer(mood_negative_s ~ 
    event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="identity"),
    control=glmerControl(calc.derivs = FALSE) )
# Summary
summary(glmer.negmood_beep)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( identity )
Formula: mood_negative_s ~ event_tot_s * activity_tot_s + activity_tot_s *      social_tot_s + physical_tot_s + ema_beep + Sex + physical_excercise_dur +  
    acc_delta + temp_mean_z + temp_slope_z + (0 + event_tot_s +      activity_tot_s + social_tot_s + physical_tot_s | castor_record_id) +  
    (0 + ema_beep | castor_record_id) + (0 + temp_slope_z | castor_record_id) +  
    (0 + temp_mean_z | castor_record_id) + (0 + acc_delta | castor_record_id) +      (0 + physical_excercise_dur | castor_record_id)
   Data: EMA_Data
Control: glmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 12654.5  12844.1  -6298.2  12596.5     5080 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.9947 -0.5958 -0.1358  0.4195  8.3307 

Random effects:
 Groups             Name                   Variance  Std.Dev. Corr             
 castor_record_id   event_tot_s            0.0034002 0.05831                   
                    activity_tot_s         0.0041612 0.06451  -0.16            
                    social_tot_s           0.0091417 0.09561  -0.19  0.01      
                    physical_tot_s         0.0093120 0.09650  -0.17  0.08 -0.24
 castor_record_id.1 ema_beep               0.0031490 0.05612                   
 castor_record_id.2 temp_slope_z           0.0026964 0.05193                   
 castor_record_id.3 temp_mean_z            0.0230049 0.15167                   
 castor_record_id.4 acc_delta              0.0001234 0.01111                   
 castor_record_id.5 physical_excercise_dur 0.0624166 0.24983                   
 Residual                                  0.1446789 0.38037                   
Number of obs: 5109, groups:  castor_record_id, 82

Fixed effects:
                             Estimate Std. Error t value Pr(>|z|)    
(Intercept)                  0.775096   0.131616   5.889 3.88e-09 ***
event_tot_s                  0.038533   0.020887   1.845   0.0651 .  
activity_tot_s               0.088208   0.028408   3.105   0.0019 ** 
social_tot_s                 0.233902   0.022812  10.254  < 2e-16 ***
physical_tot_s               0.119440   0.014848   8.044 8.68e-16 ***
ema_beep                     0.020597   0.009765   2.109   0.0349 *  
SexMale                     -0.219085   0.095448  -2.295   0.0217 *  
physical_excercise_dur      -0.188981   0.077739  -2.431   0.0151 *  
acc_delta                   -0.002205   0.002731  -0.807   0.4195    
temp_mean_z                  0.019316   0.024513   0.788   0.4307    
temp_slope_z                -0.011289   0.014402  -0.784   0.4331    
event_tot_s:activity_tot_s   0.010379   0.004196   2.473   0.0134 *  
activity_tot_s:social_tot_s -0.011324   0.003854  -2.938   0.0033 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 13 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it

Table: Mood

Now I can present a table of nelow to make it a little prettier.

tab_model(glmer.posmood_beep, glmer.negmood_beep,
         # terms=c("(Intercept)","Week_Type [Stress]", "Sex [Male]", "Program [BSc_Med]", "First_Week [Exam-First]", "acc_delta", "physical_excercise_dur"), 
          title="Table 3. HR vs Week Type", 
          transform=NULL, p.adjust = "fdr",
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
Table 3. HR vs Week Type
  mood positive s mood negative s
Predictors Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p
(Intercept) 9.74 0.20 9.35 – 10.13 48.99 <0.001 0.78 0.13 0.52 – 1.03 5.89 <0.001
event_tot_s -0.13 0.03 -0.19 – -0.06 -3.74 <0.001 0.04 0.02 -0.00 – 0.08 1.84 0.085
activity_tot_s -0.20 0.04 -0.28 – -0.12 -5.13 <0.001 0.09 0.03 0.03 – 0.14 3.11 0.006
social_tot_s -0.30 0.03 -0.35 – -0.24 -9.78 <0.001 0.23 0.02 0.19 – 0.28 10.25 <0.001
physical_tot_s -0.15 0.02 -0.19 – -0.11 -7.85 <0.001 0.12 0.01 0.09 – 0.15 8.04 <0.001
ema_beep -0.01 0.01 -0.04 – 0.01 -0.91 0.427 0.02 0.01 0.00 – 0.04 2.11 0.050
Sex [Male] 0.26 0.14 -0.01 – 0.54 1.88 0.087 -0.22 0.10 -0.41 – -0.03 -2.30 0.035
physical_excercise_dur 0.57 0.12 0.33 – 0.81 4.61 <0.001 -0.19 0.08 -0.34 – -0.04 -2.43 0.028
acc_delta 0.00 0.00 -0.00 – 0.01 1.55 0.158 -0.00 0.00 -0.01 – 0.00 -0.81 0.433
temp_mean_z -0.00 0.03 -0.05 – 0.05 -0.10 0.922 0.02 0.02 -0.03 – 0.07 0.79 0.433
temp_slope_z -0.01 0.02 -0.04 – 0.02 -0.77 0.476 -0.01 0.01 -0.04 – 0.02 -0.78 0.433
event_tot_s *
activity_tot_s
-0.02 0.01 -0.03 – -0.00 -2.76 0.009 0.01 0.00 0.00 – 0.02 2.47 0.028
activity_tot_s *
social_tot_s
0.03 0.01 0.02 – 0.04 5.06 <0.001 -0.01 0.00 -0.02 – -0.00 -2.94 0.009
Random Effects
σ2 1.12 0.14
τ00 0.02 castor_record_id 0.00 castor_record_id
0.00 castor_record_id.1 0.00 castor_record_id.1
0.00 castor_record_id.2 0.00 castor_record_id.2
0.02 castor_record_id.3 0.02 castor_record_id.3
0.00 castor_record_id.4 0.00 castor_record_id.4
0.22 castor_record_id.5 0.06 castor_record_id.5
τ11 0.01 castor_record_id.activity_tot_s 0.00 castor_record_id.activity_tot_s
0.01 castor_record_id.social_tot_s 0.01 castor_record_id.social_tot_s
0.02 castor_record_id.physical_tot_s 0.01 castor_record_id.physical_tot_s
ρ01 -0.23 castor_record_id.activity_tot_s -0.16 castor_record_id.activity_tot_s
-0.30 castor_record_id.social_tot_s -0.19 castor_record_id.social_tot_s
-0.16 castor_record_id.physical_tot_s -0.17 castor_record_id.physical_tot_s
ICC   0.74
N 82 castor_record_id 82 castor_record_id
Observations 5109 5109
Marginal R2 / Conditional R2 0.352 / NA 0.343 / 0.826

4.2.2 Skin conductance

Next we will also chekc the skin conductance measures for the moment-to-moment effects. Perhaps in the weeks the physiology measures arent increased, but in moments of stress they are. We again fit the models with different families and links, and pick the best fit which is presented here.

Tonic Mean

# Model
glmer.sc_ton_ema <- glmer(sc_tonic_mean_s ~ 
    event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="log"),
    control=glmerControl(calc.derivs = FALSE) )
failure to converge in 10000 evaluations
# Summary
summary(glmer.sc_ton_ema)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( log )
Formula: sc_tonic_mean_s ~ event_tot_s * activity_tot_s + activity_tot_s *      social_tot_s + physical_tot_s + ema_beep + Sex + physical_excercise_dur +  
    acc_delta + temp_mean_z + temp_slope_z + (0 + event_tot_s +      activity_tot_s + social_tot_s + physical_tot_s | castor_record_id) +  
    (0 + ema_beep | castor_record_id) + (0 + temp_slope_z | castor_record_id) +  
    (0 + temp_mean_z | castor_record_id) + (0 + acc_delta | castor_record_id) +      (0 + physical_excercise_dur | castor_record_id)
   Data: EMA_Data
Control: glmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
   748.9    937.1   -345.4    690.9     4842 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.1970 -0.3354 -0.1286  0.0539 17.6415 

Random effects:
 Groups             Name                   Variance  Std.Dev. Corr             
 castor_record_id   event_tot_s            0.0005510 0.02347                   
                    activity_tot_s         0.0004086 0.02021  -0.51            
                    social_tot_s           0.0005522 0.02350  -0.61 -0.07      
                    physical_tot_s         0.0005224 0.02286  -0.53  0.06 -0.03
 castor_record_id.1 ema_beep               0.0002210 0.01487                   
 castor_record_id.2 temp_slope_z           0.0036368 0.06031                   
 castor_record_id.3 temp_mean_z            0.0038344 0.06192                   
 castor_record_id.4 acc_delta              0.0001957 0.01399                   
 castor_record_id.5 physical_excercise_dur 0.0615310 0.24805                   
 Residual                                  0.0794423 0.28186                   
Number of obs: 4871, groups:  castor_record_id, 82

Fixed effects:
                              Estimate Std. Error t value Pr(>|z|)    
(Intercept)                  0.0157222  0.0531383   0.296   0.7673    
event_tot_s                  0.0088944  0.0086382   1.030   0.3032    
activity_tot_s               0.0080807  0.0106621   0.758   0.4485    
social_tot_s                 0.0038961  0.0079498   0.490   0.6241    
physical_tot_s              -0.0035858  0.0041620  -0.862   0.3889    
ema_beep                     0.0017615  0.0031239   0.564   0.5728    
SexMale                     -0.0007394  0.0192677  -0.038   0.9694    
physical_excercise_dur       0.0562354  0.0439188   1.280   0.2004    
acc_delta                    0.0175983  0.0018703   9.409  < 2e-16 ***
temp_mean_z                  0.0404021  0.0090850   4.447  8.7e-06 ***
temp_slope_z                 0.0256005  0.0092021   2.782   0.0054 ** 
event_tot_s:activity_tot_s  -0.0015035  0.0015904  -0.945   0.3445    
activity_tot_s:social_tot_s -0.0010889  0.0013955  -0.780   0.4352    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 13 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
convergence code: 0
failure to converge in 10000 evaluations

Phasic Number

# Model
glmer.sc_ph_num_ema <- glmer(sc_phasic_num  ~ 
    event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=poisson(link="sqrt"),
    control=lmerControl(calc.derivs = FALSE) )
please use glmerControl() instead of lmerControl()
# Model Summary
summary(glmer.sc_ph_num_ema)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: poisson  ( sqrt )
Formula: sc_phasic_num ~ event_tot_s * activity_tot_s + activity_tot_s *      social_tot_s + physical_tot_s + ema_beep + Sex + physical_excercise_dur +  
    acc_delta + temp_mean_z + temp_slope_z + (0 + event_tot_s +      activity_tot_s + social_tot_s + physical_tot_s | castor_record_id) +  
    (0 + ema_beep | castor_record_id) + (0 + temp_slope_z | castor_record_id) +  
    (0 + temp_mean_z | castor_record_id) + (0 + acc_delta | castor_record_id) +      (0 + physical_excercise_dur | castor_record_id)
   Data: EMA_Data
Control: lmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 80922.0  81103.8 -40433.0  80866.0     4843 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-8.4026 -2.4665 -0.9137  1.6154 19.5023 

Random effects:
 Groups             Name                   Variance Std.Dev. Corr             
 castor_record_id   event_tot_s             0.04349 0.2085                    
                    activity_tot_s          0.06333 0.2517   -0.24            
                    social_tot_s            0.04885 0.2210   -0.11 -0.51      
                    physical_tot_s          0.06791 0.2606   -0.28 -0.22 -0.05
 castor_record_id.1 ema_beep                0.04248 0.2061                    
 castor_record_id.2 temp_slope_z            0.39586 0.6292                    
 castor_record_id.3 temp_mean_z             0.67538 0.8218                    
 castor_record_id.4 acc_delta               0.01429 0.1195                    
 castor_record_id.5 physical_excercise_dur 11.02768 3.3208                    
Number of obs: 4871, groups:  castor_record_id, 82

Fixed effects:
                             Estimate Std. Error z value Pr(>|z|)    
(Intercept)                  2.102315   0.109044  19.279  < 2e-16 ***
event_tot_s                  0.043802   0.028265   1.550 0.121223    
activity_tot_s               0.061466   0.034576   1.778 0.075456 .  
social_tot_s                 0.010763   0.028890   0.373 0.709496    
physical_tot_s               0.017852   0.029628   0.603 0.546822    
ema_beep                    -0.049380   0.023363  -2.114 0.034548 *  
SexMale                      0.833191   0.110835   7.517 5.59e-14 ***
physical_excercise_dur      -0.060419   0.384936  -0.157 0.875277    
acc_delta                    0.223370   0.013428  16.635  < 2e-16 ***
temp_mean_z                  0.445457   0.091961   4.844 1.27e-06 ***
temp_slope_z                 0.245012   0.070945   3.454 0.000553 ***
event_tot_s:activity_tot_s  -0.007416   0.003124  -2.374 0.017597 *  
activity_tot_s:social_tot_s -0.008608   0.002812  -3.061 0.002204 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 13 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it

Phasic Magnitude

# Model
glmer.sc_ph_mag_ema <- glmer(sc_phasic_mag_s   ~
    event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="identity"),
    control=lmerControl(calc.derivs = FALSE) )
please use glmerControl() instead of lmerControl()
# Model Summary
summary(glmer.sc_ph_mag_ema)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( identity )
Formula: sc_phasic_mag_s ~ event_tot_s * activity_tot_s + activity_tot_s *      social_tot_s + physical_tot_s + ema_beep + Sex + physical_excercise_dur +  
    acc_delta + temp_mean_z + temp_slope_z + (0 + event_tot_s +      activity_tot_s + social_tot_s + physical_tot_s | castor_record_id) +  
    (0 + ema_beep | castor_record_id) + (0 + temp_slope_z | castor_record_id) +  
    (0 + temp_mean_z | castor_record_id) + (0 + acc_delta | castor_record_id) +      (0 + physical_excercise_dur | castor_record_id)
   Data: EMA_Data
Control: lmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 11928.1  12116.3  -5935.1  11870.1     4842 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.8549 -0.6145 -0.1341  0.4453  8.7917 

Random effects:
 Groups             Name                   Variance Std.Dev. Corr             
 castor_record_id   event_tot_s            0.003719 0.06098                   
                    activity_tot_s         0.002491 0.04991  -0.43            
                    social_tot_s           0.002295 0.04791  -0.42 -0.16      
                    physical_tot_s         0.004252 0.06521  -0.30 -0.14 -0.12
 castor_record_id.1 ema_beep               0.001755 0.04190                   
 castor_record_id.2 temp_slope_z           0.010261 0.10130                   
 castor_record_id.3 temp_mean_z            0.025211 0.15878                   
 castor_record_id.4 acc_delta              0.001430 0.03782                   
 castor_record_id.5 physical_excercise_dur 0.370433 0.60863                   
 Residual                                  0.166489 0.40803                   
Number of obs: 4871, groups:  castor_record_id, 82

Fixed effects:
                             Estimate Std. Error t value Pr(>|z|)    
(Intercept)                  1.410041   0.159517   8.839  < 2e-16 ***
event_tot_s                  0.070813   0.025461   2.781 0.005415 ** 
activity_tot_s               0.051720   0.031480   1.643 0.100388    
social_tot_s                -0.017789   0.022770  -0.781 0.434662    
physical_tot_s               0.027130   0.012434   2.182 0.029113 *  
ema_beep                    -0.002391   0.009127  -0.262 0.793329    
SexMale                      0.039797   0.071330   0.558 0.576899    
physical_excercise_dur       0.352150   0.122616   2.872 0.004079 ** 
acc_delta                    0.108003   0.005845  18.477  < 2e-16 ***
temp_mean_z                  0.122658   0.025015   4.903 9.42e-07 ***
temp_slope_z                 0.074566   0.021648   3.444 0.000572 ***
event_tot_s:activity_tot_s  -0.011383   0.004692  -2.426 0.015264 *  
activity_tot_s:social_tot_s  0.001372   0.004097   0.335 0.737664    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 13 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it

Phasic AUC

# Model
glmer.sc_ph_auc_ema <- glmer(sc_phasic_auc_s  ~
     event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="identity"),
    control=lmerControl(calc.derivs = FALSE) )
please use glmerControl() instead of lmerControl()
# Model Summary
summary(glmer.sc_ph_auc_ema)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( identity )
Formula: sc_phasic_auc_s ~ event_tot_s * activity_tot_s + activity_tot_s *      social_tot_s + physical_tot_s + ema_beep + Sex + physical_excercise_dur +  
    acc_delta + temp_mean_z + temp_slope_z + (0 + event_tot_s +      activity_tot_s + social_tot_s + physical_tot_s | castor_record_id) +  
    (0 + ema_beep | castor_record_id) + (0 + temp_slope_z | castor_record_id) +  
    (0 + temp_mean_z | castor_record_id) + (0 + acc_delta | castor_record_id) +      (0 + physical_excercise_dur | castor_record_id)
   Data: EMA_Data
Control: lmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 10457.8  10646.1  -5199.9  10399.8     4842 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.6507 -0.5402 -0.2507  0.1555  7.4885 

Random effects:
 Groups             Name                   Variance Std.Dev. Corr             
 castor_record_id   event_tot_s            0.001267 0.03560                   
                    activity_tot_s         0.002063 0.04542  -0.04            
                    social_tot_s           0.002549 0.05049  -0.59 -0.36      
                    physical_tot_s         0.002410 0.04909  -0.31 -0.44  0.10
 castor_record_id.1 ema_beep               0.001842 0.04291                   
 castor_record_id.2 temp_slope_z           0.016889 0.12996                   
 castor_record_id.3 temp_mean_z            0.026906 0.16403                   
 castor_record_id.4 acc_delta              0.002694 0.05190                   
 castor_record_id.5 physical_excercise_dur 0.185929 0.43119                   
 Residual                                  0.252030 0.50203                   
Number of obs: 4871, groups:  castor_record_id, 82

Fixed effects:
                             Estimate Std. Error t value Pr(>|z|)    
(Intercept)                  1.075483   0.152345   7.060 1.67e-12 ***
event_tot_s                  0.023499   0.023533   0.999 0.318005    
activity_tot_s               0.025375   0.029865   0.850 0.395517    
social_tot_s                 0.002950   0.021879   0.135 0.892744    
physical_tot_s               0.008871   0.010921   0.812 0.416642    
ema_beep                     0.011422   0.008897   1.284 0.199225    
SexMale                      0.045296   0.062609   0.723 0.469387    
physical_excercise_dur       0.214040   0.104933   2.040 0.041372 *  
acc_delta                    0.119242   0.007144  16.691  < 2e-16 ***
temp_mean_z                  0.125246   0.024873   5.035 4.77e-07 ***
temp_slope_z                 0.088357   0.023585   3.746 0.000179 ***
event_tot_s:activity_tot_s  -0.003589   0.004442  -0.808 0.419214    
activity_tot_s:social_tot_s -0.002404   0.003897  -0.617 0.537309    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 13 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it

Table: Skin Conductance

Now I make a table for the SC measures. I do not use FDR here, as I only do this in the finaly table we present in the artcle

tab_model(glmer.sc_ton_ema, glmer.sc_ph_num_ema, glmer.sc_ph_mag_ema, glmer.sc_ph_auc_ema,
         # terms=c("(Intercept)","Week_Type [Stress]", "Sex [Male]", "Program [BSc_Med]", "First_Week [Exam-First]", "acc_delta", "physical_excercise_dur"), 
          title="Table X. SC v Subjective Stress", 
          transform=NULL,
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
Table X. SC v Subjective Stress
  sc tonic mean s sc phasic num sc phasic mag s sc phasic auc s
Predictors Estimates std. Error CI Statistic p Log-Mean std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p
(Intercept) 0.02 0.05 -0.09 – 0.12 0.30 0.767 2.10 0.11 1.89 – 2.32 19.28 <0.001 1.41 0.16 1.10 – 1.72 8.84 <0.001 1.08 0.15 0.78 – 1.37 7.06 <0.001
event_tot_s 0.01 0.01 -0.01 – 0.03 1.03 0.303 0.04 0.03 -0.01 – 0.10 1.55 0.121 0.07 0.03 0.02 – 0.12 2.78 0.005 0.02 0.02 -0.02 – 0.07 1.00 0.318
activity_tot_s 0.01 0.01 -0.01 – 0.03 0.76 0.449 0.06 0.03 -0.01 – 0.13 1.78 0.075 0.05 0.03 -0.01 – 0.11 1.64 0.100 0.03 0.03 -0.03 – 0.08 0.85 0.396
social_tot_s 0.00 0.01 -0.01 – 0.02 0.49 0.624 0.01 0.03 -0.05 – 0.07 0.37 0.709 -0.02 0.02 -0.06 – 0.03 -0.78 0.435 0.00 0.02 -0.04 – 0.05 0.13 0.893
physical_tot_s -0.00 0.00 -0.01 – 0.00 -0.86 0.389 0.02 0.03 -0.04 – 0.08 0.60 0.547 0.03 0.01 0.00 – 0.05 2.18 0.029 0.01 0.01 -0.01 – 0.03 0.81 0.417
ema_beep 0.00 0.00 -0.00 – 0.01 0.56 0.573 -0.05 0.02 -0.10 – -0.00 -2.11 0.035 -0.00 0.01 -0.02 – 0.02 -0.26 0.793 0.01 0.01 -0.01 – 0.03 1.28 0.199
Sex [Male] -0.00 0.02 -0.04 – 0.04 -0.04 0.969 0.83 0.11 0.62 – 1.05 7.52 <0.001 0.04 0.07 -0.10 – 0.18 0.56 0.577 0.05 0.06 -0.08 – 0.17 0.72 0.469
physical_excercise_dur 0.06 0.04 -0.03 – 0.14 1.28 0.200 -0.06 0.38 -0.81 – 0.69 -0.16 0.875 0.35 0.12 0.11 – 0.59 2.87 0.004 0.21 0.10 0.01 – 0.42 2.04 0.041
acc_delta 0.02 0.00 0.01 – 0.02 9.41 <0.001 0.22 0.01 0.20 – 0.25 16.63 <0.001 0.11 0.01 0.10 – 0.12 18.48 <0.001 0.12 0.01 0.11 – 0.13 16.69 <0.001
temp_mean_z 0.04 0.01 0.02 – 0.06 4.45 <0.001 0.45 0.09 0.27 – 0.63 4.84 <0.001 0.12 0.03 0.07 – 0.17 4.90 <0.001 0.13 0.02 0.08 – 0.17 5.04 <0.001
temp_slope_z 0.03 0.01 0.01 – 0.04 2.78 0.005 0.25 0.07 0.11 – 0.38 3.45 0.001 0.07 0.02 0.03 – 0.12 3.44 0.001 0.09 0.02 0.04 – 0.13 3.75 <0.001
event_tot_s *
activity_tot_s
-0.00 0.00 -0.00 – 0.00 -0.95 0.344 -0.01 0.00 -0.01 – -0.00 -2.37 0.018 -0.01 0.00 -0.02 – -0.00 -2.43 0.015 -0.00 0.00 -0.01 – 0.01 -0.81 0.419
activity_tot_s *
social_tot_s
-0.00 0.00 -0.00 – 0.00 -0.78 0.435 -0.01 0.00 -0.01 – -0.00 -3.06 0.002 0.00 0.00 -0.01 – 0.01 0.33 0.738 -0.00 0.00 -0.01 – 0.01 -0.62 0.537
Random Effects
σ2 0.08 0.25 0.17 0.25
τ00 0.00 castor_record_id 0.04 castor_record_id 0.00 castor_record_id 0.00 castor_record_id
0.00 castor_record_id.1 0.04 castor_record_id.1 0.00 castor_record_id.1 0.00 castor_record_id.1
0.00 castor_record_id.2 0.40 castor_record_id.2 0.01 castor_record_id.2 0.02 castor_record_id.2
0.00 castor_record_id.3 0.68 castor_record_id.3 0.03 castor_record_id.3 0.03 castor_record_id.3
0.00 castor_record_id.4 0.01 castor_record_id.4 0.00 castor_record_id.4 0.00 castor_record_id.4
0.06 castor_record_id.5 11.03 castor_record_id.5 0.37 castor_record_id.5 0.19 castor_record_id.5
τ11 0.00 castor_record_id.activity_tot_s 0.06 castor_record_id.activity_tot_s 0.00 castor_record_id.activity_tot_s 0.00 castor_record_id.activity_tot_s
0.00 castor_record_id.social_tot_s 0.05 castor_record_id.social_tot_s 0.00 castor_record_id.social_tot_s 0.00 castor_record_id.social_tot_s
0.00 castor_record_id.physical_tot_s 0.07 castor_record_id.physical_tot_s 0.00 castor_record_id.physical_tot_s 0.00 castor_record_id.physical_tot_s
ρ01 -0.51 castor_record_id.activity_tot_s -0.24 castor_record_id.activity_tot_s -0.43 castor_record_id.activity_tot_s -0.04 castor_record_id.activity_tot_s
-0.61 castor_record_id.social_tot_s -0.11 castor_record_id.social_tot_s -0.42 castor_record_id.social_tot_s -0.59 castor_record_id.social_tot_s
-0.53 castor_record_id.physical_tot_s -0.28 castor_record_id.physical_tot_s -0.30 castor_record_id.physical_tot_s -0.31 castor_record_id.physical_tot_s
ICC 0.07 0.88 0.33 0.17
N 82 castor_record_id 82 castor_record_id 82 castor_record_id 82 castor_record_id
Observations 4871 4871 4871 4871
Marginal R2 / Conditional R2 0.094 / 0.161 0.417 / 0.931 0.534 / 0.690 0.532 / 0.609

4.2.3 Heart Rate

Finally we can check the heart rate and moment to moment subjective stress. Same goes as before (families and links tests, only optimal shown).

Mean

# Model
glmer.hr_mean_ema <- glmer(hr_mean_s ~
    event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="identity"),
    control=glmerControl(calc.derivs = FALSE) )
# Model Summary
summary(glmer.hr_mean_ema)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( identity )
Formula: hr_mean_s ~ event_tot_s * activity_tot_s + activity_tot_s * social_tot_s +      physical_tot_s + ema_beep + Sex + physical_excercise_dur +  
    acc_delta + temp_mean_z + temp_slope_z + (0 + event_tot_s +      activity_tot_s + social_tot_s + physical_tot_s | castor_record_id) +  
    (0 + ema_beep | castor_record_id) + (0 + temp_slope_z | castor_record_id) +  
    (0 + temp_mean_z | castor_record_id) + (0 + acc_delta | castor_record_id) +      (0 + physical_excercise_dur | castor_record_id)
   Data: EMA_Data
Control: glmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
  8717.0   8904.3  -4329.5   8659.0     4682 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.4202 -0.6003 -0.0737  0.4953 10.6267 

Random effects:
 Groups             Name                   Variance Std.Dev. Corr             
 castor_record_id   event_tot_s            0.002187 0.04677                   
                    activity_tot_s         0.001588 0.03984  -0.50            
                    social_tot_s           0.002099 0.04582  -0.16 -0.21      
                    physical_tot_s         0.002676 0.05173  -0.35  0.11 -0.31
 castor_record_id.1 ema_beep               0.001510 0.03885                   
 castor_record_id.2 temp_slope_z           0.011105 0.10538                   
 castor_record_id.3 temp_mean_z            0.020745 0.14403                   
 castor_record_id.4 acc_delta              0.001057 0.03252                   
 castor_record_id.5 physical_excercise_dur 0.181223 0.42570                   
 Residual                                  0.029608 0.17207                   
Number of obs: 4711, groups:  castor_record_id, 82

Fixed effects:
                             Estimate Std. Error t value Pr(>|z|)    
(Intercept)                  3.259889   0.115826  28.145  < 2e-16 ***
event_tot_s                  0.013262   0.018356   0.723   0.4700    
activity_tot_s              -0.010007   0.022837  -0.438   0.6612    
social_tot_s                -0.028652   0.016813  -1.704   0.0884 .  
physical_tot_s               0.016316   0.009320   1.751   0.0800 .  
ema_beep                    -0.044789   0.007175  -6.242 4.31e-10 ***
SexMale                     -0.004925   0.061770  -0.080   0.9365    
physical_excercise_dur       0.462712   0.086796   5.331 9.77e-08 ***
acc_delta                    0.142871   0.004758  30.030  < 2e-16 ***
temp_mean_z                 -0.093975   0.021275  -4.417 1.00e-05 ***
temp_slope_z                 0.032899   0.019330   1.702   0.0888 .  
event_tot_s:activity_tot_s  -0.001799   0.003417  -0.526   0.5987    
activity_tot_s:social_tot_s  0.004116   0.002982   1.380   0.1675    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 13 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it

Min

# Model
glmer.hr_min_ema <- glmer(hr_min_s  ~
    event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="log"),
    control=lmerControl(calc.derivs = FALSE) )
please use glmerControl() instead of lmerControl()
# Model Summary
summary(glmer.hr_min_ema)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( log )
Formula: hr_min_s ~ event_tot_s * activity_tot_s + activity_tot_s * social_tot_s +      physical_tot_s + ema_beep + Sex + physical_excercise_dur +  
    acc_delta + temp_mean_z + temp_slope_z + (0 + event_tot_s +      activity_tot_s + social_tot_s + physical_tot_s | castor_record_id) +  
    (0 + ema_beep | castor_record_id) + (0 + temp_slope_z | castor_record_id) +  
    (0 + temp_mean_z | castor_record_id) + (0 + acc_delta | castor_record_id) +      (0 + physical_excercise_dur | castor_record_id)
   Data: EMA_Data
Control: lmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 10945.0  11132.2  -5443.5  10887.0     4682 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.1763 -0.6460 -0.0478  0.5441  9.3277 

Random effects:
 Groups             Name                   Variance  Std.Dev. Corr             
 castor_record_id   event_tot_s            8.710e-05 0.009333                  
                    activity_tot_s         5.750e-05 0.007583  0.51            
                    social_tot_s           1.709e-04 0.013071  0.14 -0.78      
                    physical_tot_s         3.865e-04 0.019659 -0.55 -0.11 -0.27
 castor_record_id.1 ema_beep               1.676e-04 0.012948                  
 castor_record_id.2 temp_slope_z           1.106e-03 0.033264                  
 castor_record_id.3 temp_mean_z            2.010e-03 0.044828                  
 castor_record_id.4 acc_delta              4.644e-05 0.006814                  
 castor_record_id.5 physical_excercise_dur 1.694e-02 0.130158                  
 Residual                                  4.323e-02 0.207909                  
Number of obs: 4711, groups:  castor_record_id, 82

Fixed effects:
                              Estimate Std. Error t value Pr(>|z|)    
(Intercept)                  1.3502304  0.0396461  34.057  < 2e-16 ***
event_tot_s                 -0.0011512  0.0061120  -0.188 0.850607    
activity_tot_s              -0.0107717  0.0076745  -1.404 0.160447    
social_tot_s                -0.0128868  0.0055910  -2.305 0.021171 *  
physical_tot_s               0.0028280  0.0033193   0.852 0.394220    
ema_beep                    -0.0118784  0.0024391  -4.870 1.12e-06 ***
SexMale                     -0.0750942  0.0200708  -3.741 0.000183 ***
physical_excercise_dur       0.1059833  0.0278223   3.809 0.000139 ***
acc_delta                    0.0218142  0.0011148  19.568  < 2e-16 ***
temp_mean_z                  0.0117941  0.0068140   1.731 0.083477 .  
temp_slope_z                 0.0096380  0.0061063   1.578 0.114477    
event_tot_s:activity_tot_s  -0.0001731  0.0011610  -0.149 0.881505    
activity_tot_s:social_tot_s  0.0017559  0.0009926   1.769 0.076883 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 13 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it

Max

# Model
glmer.hr_max_ema <- glmer(hr_max_s ~
    event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="identity"),
    control=lmerControl(calc.derivs = FALSE) )
please use glmerControl() instead of lmerControl()
# Model Summary
summary(glmer.hr_max_ema)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( identity )
Formula: hr_max_s ~ event_tot_s * activity_tot_s + activity_tot_s * social_tot_s +      physical_tot_s + ema_beep + Sex + physical_excercise_dur +  
    acc_delta + temp_mean_z + temp_slope_z + (0 + event_tot_s +      activity_tot_s + social_tot_s + physical_tot_s | castor_record_id) +  
    (0 + ema_beep | castor_record_id) + (0 + temp_slope_z | castor_record_id) +  
    (0 + temp_mean_z | castor_record_id) + (0 + acc_delta | castor_record_id) +      (0 + physical_excercise_dur | castor_record_id)
   Data: EMA_Data
Control: lmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 12054.5  12241.8  -5998.3  11996.5     4682 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.0029 -0.6366 -0.1348  0.4838  7.5959 

Random effects:
 Groups             Name                   Variance Std.Dev. Corr             
 castor_record_id   event_tot_s            0.004771 0.06907                   
                    activity_tot_s         0.002638 0.05136  -0.68            
                    social_tot_s           0.004083 0.06390  -0.07 -0.33      
                    physical_tot_s         0.004273 0.06537  -0.67  0.60 -0.50
 castor_record_id.1 ema_beep               0.002061 0.04540                   
 castor_record_id.2 temp_slope_z           0.019433 0.13940                   
 castor_record_id.3 temp_mean_z            0.034834 0.18664                   
 castor_record_id.4 acc_delta              0.001353 0.03678                   
 castor_record_id.5 physical_excercise_dur 0.429877 0.65565                   
 Residual                                  0.048187 0.21951                   
Number of obs: 4711, groups:  castor_record_id, 82

Fixed effects:
                              Estimate Std. Error t value Pr(>|z|)    
(Intercept)                  3.3903417  0.1613062  21.018  < 2e-16 ***
event_tot_s                  0.0153649  0.0258572   0.594  0.55237    
activity_tot_s               0.0270551  0.0319920   0.846  0.39773    
social_tot_s                -0.0004125  0.0235979  -0.017  0.98605    
physical_tot_s               0.0056451  0.0125522   0.450  0.65291    
ema_beep                    -0.0521387  0.0095804  -5.442 5.26e-08 ***
SexMale                      0.1540406  0.0672158   2.292  0.02192 *  
physical_excercise_dur       0.4189564  0.1277727   3.279  0.00104 ** 
acc_delta                    0.1770121  0.0060781  29.123  < 2e-16 ***
temp_mean_z                 -0.2266377  0.0284757  -7.959 1.73e-15 ***
temp_slope_z                 0.0299362  0.0269722   1.110  0.26705    
event_tot_s:activity_tot_s  -0.0029616  0.0048020  -0.617  0.53740    
activity_tot_s:social_tot_s -0.0007412  0.0042060  -0.176  0.86012    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 13 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it

Table: Heart Rate

We now make a table for the heart rate measures for easier visualization.

tab_model(glmer.hr_mean_ema, glmer.hr_min_ema, glmer.hr_max_ema, 
          dv.labels=c("Mean", "Min", "Max"), 
          title="Table X. Heart rate vs. Subjective Stress",
            transform=NULL, 
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
Table X. Heart rate vs. Subjective Stress
  Mean Min Max
Predictors Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p
(Intercept) 3.26 0.12 3.03 – 3.49 28.14 <0.001 1.35 0.04 1.27 – 1.43 34.06 <0.001 3.39 0.16 3.07 – 3.71 21.02 <0.001
event_tot_s 0.01 0.02 -0.02 – 0.05 0.72 0.470 -0.00 0.01 -0.01 – 0.01 -0.19 0.851 0.02 0.03 -0.04 – 0.07 0.59 0.552
activity_tot_s -0.01 0.02 -0.05 – 0.03 -0.44 0.661 -0.01 0.01 -0.03 – 0.00 -1.40 0.160 0.03 0.03 -0.04 – 0.09 0.85 0.398
social_tot_s -0.03 0.02 -0.06 – 0.00 -1.70 0.088 -0.01 0.01 -0.02 – -0.00 -2.30 0.021 -0.00 0.02 -0.05 – 0.05 -0.02 0.986
physical_tot_s 0.02 0.01 -0.00 – 0.03 1.75 0.080 0.00 0.00 -0.00 – 0.01 0.85 0.394 0.01 0.01 -0.02 – 0.03 0.45 0.653
ema_beep -0.04 0.01 -0.06 – -0.03 -6.24 <0.001 -0.01 0.00 -0.02 – -0.01 -4.87 <0.001 -0.05 0.01 -0.07 – -0.03 -5.44 <0.001
Sex [Male] -0.00 0.06 -0.13 – 0.12 -0.08 0.936 -0.08 0.02 -0.11 – -0.04 -3.74 <0.001 0.15 0.07 0.02 – 0.29 2.29 0.022
physical_excercise_dur 0.46 0.09 0.29 – 0.63 5.33 <0.001 0.11 0.03 0.05 – 0.16 3.81 <0.001 0.42 0.13 0.17 – 0.67 3.28 0.001
acc_delta 0.14 0.00 0.13 – 0.15 30.03 <0.001 0.02 0.00 0.02 – 0.02 19.57 <0.001 0.18 0.01 0.17 – 0.19 29.12 <0.001
temp_mean_z -0.09 0.02 -0.14 – -0.05 -4.42 <0.001 0.01 0.01 -0.00 – 0.03 1.73 0.083 -0.23 0.03 -0.28 – -0.17 -7.96 <0.001
temp_slope_z 0.03 0.02 -0.00 – 0.07 1.70 0.089 0.01 0.01 -0.00 – 0.02 1.58 0.114 0.03 0.03 -0.02 – 0.08 1.11 0.267
event_tot_s *
activity_tot_s
-0.00 0.00 -0.01 – 0.00 -0.53 0.599 -0.00 0.00 -0.00 – 0.00 -0.15 0.882 -0.00 0.00 -0.01 – 0.01 -0.62 0.537
activity_tot_s *
social_tot_s
0.00 0.00 -0.00 – 0.01 1.38 0.167 0.00 0.00 -0.00 – 0.00 1.77 0.077 -0.00 0.00 -0.01 – 0.01 -0.18 0.860
Random Effects
σ2 0.03 0.04 0.05
τ00 0.00 castor_record_id 0.00 castor_record_id 0.00 castor_record_id
0.00 castor_record_id.1 0.00 castor_record_id.1 0.00 castor_record_id.1
0.01 castor_record_id.2 0.00 castor_record_id.2 0.02 castor_record_id.2
0.02 castor_record_id.3 0.00 castor_record_id.3 0.03 castor_record_id.3
0.00 castor_record_id.4 0.00 castor_record_id.4 0.00 castor_record_id.4
0.18 castor_record_id.5 0.02 castor_record_id.5 0.43 castor_record_id.5
τ11 0.00 castor_record_id.activity_tot_s 0.00 castor_record_id.activity_tot_s 0.00 castor_record_id.activity_tot_s
0.00 castor_record_id.social_tot_s 0.00 castor_record_id.social_tot_s 0.00 castor_record_id.social_tot_s
0.00 castor_record_id.physical_tot_s 0.00 castor_record_id.physical_tot_s 0.00 castor_record_id.physical_tot_s
ρ01 -0.50 castor_record_id.activity_tot_s 0.51 castor_record_id.activity_tot_s -0.68 castor_record_id.activity_tot_s
-0.16 castor_record_id.social_tot_s 0.14 castor_record_id.social_tot_s -0.07 castor_record_id.social_tot_s
-0.35 castor_record_id.physical_tot_s -0.55 castor_record_id.physical_tot_s -0.67 castor_record_id.physical_tot_s
ICC 0.70   0.58
N 82 castor_record_id 82 castor_record_id 82 castor_record_id
Observations 4711 4711 4711
Marginal R2 / Conditional R2 0.843 / 0.952 0.239 / NA 0.882 / 0.950

4.2.4 Table: Physiology v Subjective Stress

We now build the table for all the physiology measures, and apply the FDR correction to these models. These are the statistics we report in the article.

tab_model(glmer.sc_ton_ema, glmer.sc_ph_num_ema, glmer.sc_ph_mag_ema, glmer.sc_ph_auc_ema, 
            glmer.hr_mean_ema, glmer.hr_min_ema, glmer.hr_max_ema, 
          dv.labels=c("SC Tonic", "SC Number", "SC Magnitude", "SC AUC", "HR Mean", "HR Min", "HR Max"), 
          title="Table X. Momentary Physiology and Subjective Stress",
            transform=NULL, p.adjust="fdr", 
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
Table X. Momentary Physiology and Subjective Stress
  SC Tonic SC Number SC Magnitude SC AUC HR Mean HR Min HR Max
Predictors Estimates std. Error CI Statistic p Log-Mean std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p
(Intercept) 0.02 0.05 -0.09 – 0.12 0.30 0.831 2.10 0.11 1.89 – 2.32 19.28 <0.001 1.41 0.16 1.10 – 1.72 8.84 <0.001 1.08 0.15 0.78 – 1.37 7.06 <0.001 3.26 0.12 3.03 – 3.49 28.14 <0.001 1.35 0.04 1.27 – 1.43 34.06 <0.001 3.39 0.16 3.07 – 3.71 21.02 <0.001
event_tot_s 0.01 0.01 -0.01 – 0.03 1.03 0.648 0.04 0.03 -0.01 – 0.10 1.55 0.158 0.07 0.03 0.02 – 0.12 2.78 0.012 0.02 0.02 -0.02 – 0.07 1.00 0.545 0.01 0.02 -0.02 – 0.05 0.72 0.611 -0.00 0.01 -0.01 – 0.01 -0.19 0.882 0.02 0.03 -0.04 – 0.07 0.59 0.718
activity_tot_s 0.01 0.01 -0.01 – 0.03 0.76 0.648 0.06 0.03 -0.01 – 0.13 1.78 0.109 0.05 0.03 -0.01 – 0.11 1.64 0.145 0.03 0.03 -0.03 – 0.08 0.85 0.545 -0.01 0.02 -0.05 – 0.03 -0.44 0.716 -0.01 0.01 -0.03 – 0.00 -1.40 0.209 0.03 0.03 -0.04 – 0.09 0.85 0.646
social_tot_s 0.00 0.01 -0.01 – 0.02 0.49 0.738 0.01 0.03 -0.05 – 0.07 0.37 0.769 -0.02 0.02 -0.06 – 0.03 -0.78 0.565 0.00 0.02 -0.04 – 0.05 0.13 0.893 -0.03 0.02 -0.06 – 0.00 -1.70 0.144 -0.01 0.01 -0.02 – -0.00 -2.30 0.046 -0.00 0.02 -0.05 – 0.05 -0.02 0.986
physical_tot_s -0.00 0.00 -0.01 – 0.00 -0.86 0.648 0.02 0.03 -0.04 – 0.08 0.60 0.646 0.03 0.01 0.00 – 0.05 2.18 0.047 0.01 0.01 -0.01 – 0.03 0.81 0.545 0.02 0.01 -0.00 – 0.03 1.75 0.144 0.00 0.00 -0.00 – 0.01 0.85 0.466 0.01 0.01 -0.02 – 0.03 0.45 0.772
ema_beep 0.00 0.00 -0.00 – 0.01 0.56 0.738 -0.05 0.02 -0.10 – -0.00 -2.11 0.056 -0.00 0.01 -0.02 – 0.02 -0.26 0.793 0.01 0.01 -0.01 – 0.03 1.28 0.432 -0.04 0.01 -0.06 – -0.03 -6.24 <0.001 -0.01 0.00 -0.02 – -0.01 -4.87 <0.001 -0.05 0.01 -0.07 – -0.03 -5.44 <0.001
Sex [Male] -0.00 0.02 -0.04 – 0.04 -0.04 0.969 0.83 0.11 0.62 – 1.05 7.52 <0.001 0.04 0.07 -0.10 – 0.18 0.56 0.682 0.05 0.06 -0.08 – 0.17 0.72 0.555 -0.00 0.06 -0.13 – 0.12 -0.08 0.936 -0.08 0.02 -0.11 – -0.04 -3.74 <0.001 0.15 0.07 0.02 – 0.29 2.29 0.047
physical_excercise_dur 0.06 0.04 -0.03 – 0.14 1.28 0.648 -0.06 0.38 -0.81 – 0.69 -0.16 0.875 0.35 0.12 0.11 – 0.59 2.87 0.011 0.21 0.10 0.01 – 0.42 2.04 0.108 0.46 0.09 0.29 – 0.63 5.33 <0.001 0.11 0.03 0.05 – 0.16 3.81 <0.001 0.42 0.13 0.17 – 0.67 3.28 0.003
acc_delta 0.02 0.00 0.01 – 0.02 9.41 <0.001 0.22 0.01 0.20 – 0.25 16.63 <0.001 0.11 0.01 0.10 – 0.12 18.48 <0.001 0.12 0.01 0.11 – 0.13 16.69 <0.001 0.14 0.00 0.13 – 0.15 30.03 <0.001 0.02 0.00 0.02 – 0.02 19.57 <0.001 0.18 0.01 0.17 – 0.19 29.12 <0.001
temp_mean_z 0.04 0.01 0.02 – 0.06 4.45 <0.001 0.45 0.09 0.27 – 0.63 4.84 <0.001 0.12 0.03 0.07 – 0.17 4.90 <0.001 0.13 0.02 0.08 – 0.17 5.04 <0.001 -0.09 0.02 -0.14 – -0.05 -4.42 <0.001 0.01 0.01 -0.00 – 0.03 1.73 0.136 -0.23 0.03 -0.28 – -0.17 -7.96 <0.001
temp_slope_z 0.03 0.01 0.01 – 0.04 2.78 0.023 0.25 0.07 0.11 – 0.38 3.45 0.001 0.07 0.02 0.03 – 0.12 3.44 0.002 0.09 0.02 0.04 – 0.13 3.75 0.001 0.03 0.02 -0.00 – 0.07 1.70 0.144 0.01 0.01 -0.00 – 0.02 1.58 0.165 0.03 0.03 -0.02 – 0.08 1.11 0.496
event_tot_s *
activity_tot_s
-0.00 0.00 -0.00 – 0.00 -0.95 0.648 -0.01 0.00 -0.01 – -0.00 -2.37 0.033 -0.01 0.00 -0.02 – -0.00 -2.43 0.028 -0.00 0.00 -0.01 – 0.01 -0.81 0.545 -0.00 0.00 -0.01 – 0.00 -0.53 0.708 -0.00 0.00 -0.00 – 0.00 -0.15 0.882 -0.00 0.00 -0.01 – 0.01 -0.62 0.718
activity_tot_s *
social_tot_s
-0.00 0.00 -0.00 – 0.00 -0.78 0.648 -0.01 0.00 -0.01 – -0.00 -3.06 0.005 0.00 0.00 -0.01 – 0.01 0.33 0.793 -0.00 0.00 -0.01 – 0.01 -0.62 0.582 0.00 0.00 -0.00 – 0.01 1.38 0.242 0.00 0.00 -0.00 – 0.00 1.77 0.136 -0.00 0.00 -0.01 – 0.01 -0.18 0.932
Random Effects
σ2 0.08 0.25 0.17 0.25 0.03 0.04 0.05
τ00 0.00 castor_record_id 0.04 castor_record_id 0.00 castor_record_id 0.00 castor_record_id 0.00 castor_record_id 0.00 castor_record_id 0.00 castor_record_id
0.00 castor_record_id.1 0.04 castor_record_id.1 0.00 castor_record_id.1 0.00 castor_record_id.1 0.00 castor_record_id.1 0.00 castor_record_id.1 0.00 castor_record_id.1
0.00 castor_record_id.2 0.40 castor_record_id.2 0.01 castor_record_id.2 0.02 castor_record_id.2 0.01 castor_record_id.2 0.00 castor_record_id.2 0.02 castor_record_id.2
0.00 castor_record_id.3 0.68 castor_record_id.3 0.03 castor_record_id.3 0.03 castor_record_id.3 0.02 castor_record_id.3 0.00 castor_record_id.3 0.03 castor_record_id.3
0.00 castor_record_id.4 0.01 castor_record_id.4 0.00 castor_record_id.4 0.00 castor_record_id.4 0.00 castor_record_id.4 0.00 castor_record_id.4 0.00 castor_record_id.4
0.06 castor_record_id.5 11.03 castor_record_id.5 0.37 castor_record_id.5 0.19 castor_record_id.5 0.18 castor_record_id.5 0.02 castor_record_id.5 0.43 castor_record_id.5
τ11 0.00 castor_record_id.activity_tot_s 0.06 castor_record_id.activity_tot_s 0.00 castor_record_id.activity_tot_s 0.00 castor_record_id.activity_tot_s 0.00 castor_record_id.activity_tot_s 0.00 castor_record_id.activity_tot_s 0.00 castor_record_id.activity_tot_s
0.00 castor_record_id.social_tot_s 0.05 castor_record_id.social_tot_s 0.00 castor_record_id.social_tot_s 0.00 castor_record_id.social_tot_s 0.00 castor_record_id.social_tot_s 0.00 castor_record_id.social_tot_s 0.00 castor_record_id.social_tot_s
0.00 castor_record_id.physical_tot_s 0.07 castor_record_id.physical_tot_s 0.00 castor_record_id.physical_tot_s 0.00 castor_record_id.physical_tot_s 0.00 castor_record_id.physical_tot_s 0.00 castor_record_id.physical_tot_s 0.00 castor_record_id.physical_tot_s
ρ01 -0.51 castor_record_id.activity_tot_s -0.24 castor_record_id.activity_tot_s -0.43 castor_record_id.activity_tot_s -0.04 castor_record_id.activity_tot_s -0.50 castor_record_id.activity_tot_s 0.51 castor_record_id.activity_tot_s -0.68 castor_record_id.activity_tot_s
-0.61 castor_record_id.social_tot_s -0.11 castor_record_id.social_tot_s -0.42 castor_record_id.social_tot_s -0.59 castor_record_id.social_tot_s -0.16 castor_record_id.social_tot_s 0.14 castor_record_id.social_tot_s -0.07 castor_record_id.social_tot_s
-0.53 castor_record_id.physical_tot_s -0.28 castor_record_id.physical_tot_s -0.30 castor_record_id.physical_tot_s -0.31 castor_record_id.physical_tot_s -0.35 castor_record_id.physical_tot_s -0.55 castor_record_id.physical_tot_s -0.67 castor_record_id.physical_tot_s
ICC 0.07 0.88 0.33 0.17 0.70   0.58
N 82 castor_record_id 82 castor_record_id 82 castor_record_id 82 castor_record_id 82 castor_record_id 82 castor_record_id 82 castor_record_id
Observations 4871 4871 4871 4871 4711 4711 4711
Marginal R2 / Conditional R2 0.094 / 0.161 0.417 / 0.931 0.534 / 0.690 0.532 / 0.609 0.843 / 0.952 0.239 / NA 0.882 / 0.950

4.2.5 Plot: Outcomes v Subjective Stress

Next we plot our outcomes as a function of the subjective stress. We build four graphs, one for each of the subjective stress types. These graphs are presented in the results section of the article (figure 3).

# Shorrtlist the variables to those of interest
plot.vars <- plot_models(glmer.posmood_beep, glmer.sc_ph_num_ema, glmer.hr_mean_ema, glmer.hr_min_ema, glmer.hr_max_ema)
# Get and filter terms
full_term <- as.vector(plot.vars$data$term[1:length(plot.vars$data$term)])
event_term <- full_term[full_term != "event_tot_s"]
activ_term <-full_term[full_term != "activity_tot_s"]
soc_term <- full_term[full_term != "social_tot_s"]
phy_term <- full_term[full_term != "physical_tot_s"]
# Set the colours
col_list <-c('#7570B3','#7570B3','#7570B3',"#D95F02", "#D95F02", '#D95F02', '#D95F02', "#1B9E77", "#1B9E77")
# Event Plot
plot.event_substr <- plot_models(glmer.posmood_beep, glmer.negmood_beep, 
            glmer.sc_ton_ema, glmer.sc_ph_num_ema, glmer.sc_ph_mag_ema, glmer.sc_ph_auc_ema, 
            glmer.hr_mean_ema, glmer.hr_min_ema, glmer.hr_max_ema, 
            m.labels=c("Positive Affect", "Negative Affect", "SC Tonic", "SC Number", "SC Magnitued", "SC AUC", "HR Mean", "HR Minimum", "HR Maximum"),
            axis.labels = c(""), 
            # Stastistical Stuff
            rm.terms = event_term,
            #show.values = T,
            #value.size = 4, 
            #std.est=T, 
            show.p=T,
            p.shape=T,
            p.adjust = "fdr", 
            legend.pval.title = "Significance", 
            # Visual Stuff
            colors=col_list,
            dot.size=2,
            line.size = 0.5,
            spacing=0.7, 
            vline.color = "darkgrey", 
            legend.title = "") + 
            ptheme + 
            theme(axis.ticks.y=element_blank(), 
                  axis.title = element_text(size=16),axis.text.x=element_text(size=11),
                  panel.grid.major.x = element_line(colour = "grey95"),
                  panel.grid.minor.x = element_line(colour = "grey90")) 
plot.event_substr <- plot.event_substr+ coord_flip(ylim=c(0.75,1.25)) +  coord_flip(ylim=c(-0.5,0.5)) + theme(panel.grid.major.y = element_blank(), panel.grid.minor.y = element_blank())
Coordinate system already present. Adding new coordinate system, which will replace the existing one.
Coordinate system already present. Adding new coordinate system, which will replace the existing one.
#ggsave("figures/fig_StrResid_Event.tiff", units="in", width=4, height=4, dpi=300, compression = 'lzw', bg="transparent")
# Act Plot
plot.activity_substr <-  plot_models(glmer.posmood_beep, glmer.negmood_beep, 
            glmer.sc_ton_ema, glmer.sc_ph_num_ema, glmer.sc_ph_mag_ema, glmer.sc_ph_auc_ema, 
            glmer.hr_mean_ema, glmer.hr_min_ema, glmer.hr_max_ema, 
            m.labels=c("Positive Affect", "Negative Affect", "SC Tonic", "SC Number", "SC Magnitued", "SC AUC", "HR Mean", "HR Minimum", "HR Maximum"),
            axis.labels = c(""), 
            # Stastistical Stuff
            rm.terms = activ_term,
            #show.values = T,
            #value.size = 4, 
            #std.est=T, 
            show.p=T,
            p.shape=T,
            p.adjust = "fdr", 
            legend.pval.title = "Significance", 
            # Visual Stuff
            colors=col_list,
            dot.size=2,
            line.size = 0.5,
            spacing=0.7, 
            vline.color = "darkgrey", 
            legend.title = "") + 
            ptheme + 
              theme(axis.ticks.y=element_blank(), 
                  axis.title = element_text(size=16),axis.text.x=element_text(size=11),
                  panel.grid.major.x = element_line(colour = "grey95"),
                  panel.grid.minor.x = element_line(colour = "grey90")) 
plot.activity_substr <- plot.activity_substr+ coord_flip(ylim=c(0.75,1.25)) +  coord_flip(ylim=c(-0.5,0.5)) + theme(panel.grid.major.y = element_blank(), panel.grid.minor.y = element_blank())
Coordinate system already present. Adding new coordinate system, which will replace the existing one.
Coordinate system already present. Adding new coordinate system, which will replace the existing one.
#ggsave("figures/fig_StrResid_Activity.tiff", units="in", width=4, height=4, dpi=300, compression = 'lzw', bg="transparent")
# Social Stress
plot.social_substr <-  plot_models(glmer.posmood_beep, glmer.negmood_beep, 
            glmer.sc_ton_ema, glmer.sc_ph_num_ema, glmer.sc_ph_mag_ema, glmer.sc_ph_auc_ema, 
            glmer.hr_mean_ema, glmer.hr_min_ema, glmer.hr_max_ema, 
            m.labels=c("Positive Affect", "Negative Affect", "SC Tonic", "SC Number", "SC Magnitued", "SC AUC", "HR Mean", "HR Minimum", "HR Maximum"),
            axis.labels = c(""), 
            # Stastistical Stuff
            rm.terms = soc_term,
            #show.values = T,
            #value.size = 4, 
            #std.est=T, 
            show.p=T,
            p.shape=T,
            p.adjust = "fdr", 
            legend.pval.title = "Significance", 
            # Visual Stuff
            colors=col_list,
            dot.size=2,
            line.size = 0.5,
            spacing=0.7, 
            vline.color = "darkgrey", 
            legend.title = "") + 
            ptheme + 
            theme(axis.ticks.y=element_blank(), 
                  axis.title = element_text(size=16),axis.text.x=element_text(size=11),
                  panel.grid.major.x = element_line(colour = "grey95"),
                  panel.grid.minor.x = element_line(colour = "grey90")) 
## Plot
plot.social_substr <- plot.social_substr + coord_flip(ylim=c(0.75,1.25)) +  coord_flip(ylim=c(-0.5,0.5)) + theme(panel.grid.major.y = element_blank(), panel.grid.minor.y = element_blank())
Coordinate system already present. Adding new coordinate system, which will replace the existing one.
Coordinate system already present. Adding new coordinate system, which will replace the existing one.
#ggsave("figures/fig_StrResid_Social.tiff", units="in", width=4, height=4, dpi=300, compression = 'lzw', bg="transparent")
# Physical Stress
plot.physical_substr <- plot_models(glmer.posmood_beep, glmer.negmood_beep, 
            glmer.sc_ton_ema, glmer.sc_ph_num_ema, glmer.sc_ph_mag_ema, glmer.sc_ph_auc_ema, 
            glmer.hr_mean_ema, glmer.hr_min_ema, glmer.hr_max_ema, 
            m.labels=c("Positive Affect", "Negative Affect", "SC Tonic", "SC Number", "SC Magnitued", "SC AUC", "HR Mean", "HR Minimum", "HR Maximum"),
            axis.labels = c(""), 
            # Stastistical Stuff
            rm.terms = phy_term,
            #show.values = T,
            #value.size = 4, 
            #std.est=T, 
            show.p=T,
            p.shape=T,
            p.adjust = "fdr", 
            legend.pval.title = "Significance", 
            # Visual Stuff
            colors=col_list,
            dot.size=2,
            line.size =0.5,
            spacing=0.7, 
            vline.color = "darkgrey", 
            legend.title = "") + 
            ptheme + 
              theme(axis.ticks.y=element_blank(), 
                  axis.title = element_text(size=16),axis.text.x=element_text(size=11),
                  panel.grid.major.x = element_line(colour = "grey95"),
                  panel.grid.minor.x = element_line(colour = "grey90")) 
# Plot
plot.physical_substr <- plot.physical_substr +  coord_flip(ylim=c(-0.5,0.5), xlim=c(1,1.1)) + theme(panel.grid.major.y = element_blank(), panel.grid.minor.y = element_blank())
Coordinate system already present. Adding new coordinate system, which will replace the existing one.
#ggsave("figures/fig_StrResid_Physical.tiff", units="in", width=4, height=4, dpi=300, compression = 'lzw', bg="transparent")
# All
ggarrange(plot.event_substr, plot.activity_substr, plot.social_substr, plot.physical_substr, common.legend = T, legend="right")
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#ggsave("figures/fig_StrResid_MAT.tiff", units="in", width=7, height=7, dpi=300, compression = 'lzw', bg="transparent")

So we only see event related and physical stress have a relationship with SC magnitude. Thats cools, and somewhat replicates some previous findings from Smets et al. 2018.

4.3 Mood and Physio

Since we think this is an arousal related mechanism, we would also need to establish the link to physiology. To this end, we check the relationship between physiology and the mood items. We see a high correlation between positive and negative mood (presented below). So we also model interaction terms here. Due to model convergence issues, we only model the fixed intercepts here for the fixe effects of interest. Again, we check all model families before we pick the one with the best fit.

4.3.1 Skin Conductance

Tonic Mean

# Model
glmer.sc_ton_mood <- glmer(sc_tonic_mean_s ~ mood_positive_s*mood_negative_s + 
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex + temp_slope_z + temp_mean_z + 
    acc_delta + physical_excercise_dur +
    (0+mood_positive_s*mood_negative_s| castor_record_id) +# + (1+mood_negative_s|castor_record_id)+
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="log"),
    control=glmerControl(calc.derivs = FALSE) )
# Summary
summary(glmer.sc_ton_mood)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( log )
Formula: sc_tonic_mean_s ~ mood_positive_s * mood_negative_s + ema_beep +      Sex + temp_slope_z + temp_mean_z + acc_delta + physical_excercise_dur +  
    (0 + mood_positive_s * mood_negative_s | castor_record_id) +      (0 + ema_beep | castor_record_id) + (0 + temp_slope_z | castor_record_id) +  
    (0 + temp_mean_z | castor_record_id) + (0 + acc_delta | castor_record_id) +      (0 + physical_excercise_dur | castor_record_id)
   Data: EMA_Data
Control: glmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
   826.0    968.8   -391.0    782.0     4849 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.1179 -0.3349 -0.1231  0.0591 19.0949 

Random effects:
 Groups             Name                            Variance  Std.Dev. Corr       
 castor_record_id   mood_positive_s                 0.0002771 0.01665             
                    mood_negative_s                 0.0011174 0.03343   0.49      
                    mood_positive_s:mood_negative_s 0.0001141 0.01068  -0.83 -0.88
 castor_record_id.1 ema_beep                        0.0002370 0.01540             
 castor_record_id.2 temp_slope_z                    0.0039451 0.06281             
 castor_record_id.3 temp_mean_z                     0.0038193 0.06180             
 castor_record_id.4 acc_delta                       0.0001949 0.01396             
 castor_record_id.5 physical_excercise_dur          0.0741943 0.27239             
 Residual                                           0.0838519 0.28957             
Number of obs: 4871, groups:  castor_record_id, 82

Fixed effects:
                                  Estimate Std. Error t value Pr(>|z|)    
(Intercept)                      0.0396304  0.0438377   0.904  0.36598    
mood_positive_s                  0.0042376  0.0064384   0.658  0.51042    
mood_negative_s                 -0.0050873  0.0115797  -0.439  0.66042    
ema_beep                         0.0021828  0.0031432   0.694  0.48739    
SexMale                         -0.0153771  0.0194991  -0.789  0.43034    
temp_slope_z                     0.0306751  0.0095179   3.223  0.00127 ** 
temp_mean_z                      0.0428873  0.0091208   4.702 2.57e-06 ***
acc_delta                        0.0186543  0.0018802   9.922  < 2e-16 ***
physical_excercise_dur           0.0767597  0.0465881   1.648  0.09943 .  
mood_positive_s:mood_negative_s -0.0007453  0.0022761  -0.327  0.74333    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) md_ps_ md_ng_ ema_bp SexMal tmp_s_ tmp_m_ acc_dl phys__
mood_pstv_s -0.864                                                        
mood_ngtv_s -0.734  0.807                                                 
ema_beep    -0.115 -0.069 -0.043                                          
SexMale     -0.191 -0.003  0.033  0.005                                   
temp_slop_z -0.016  0.006  0.008 -0.009 -0.004                            
temp_mean_z  0.028 -0.021 -0.005 -0.088 -0.022  0.030                     
acc_delta   -0.062 -0.012 -0.004  0.037 -0.010  0.055  0.064              
physcl_xcr_  0.007 -0.042 -0.017 -0.005  0.011  0.001  0.018  0.000       
md_pstv_:__  0.504 -0.746 -0.890  0.036  0.004 -0.007  0.001  0.008  0.019

Phasic Number

# Summary
summary(glmer.sc_phnum_mood)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( identity )
Formula: sc_phasic_num_s ~ mood_positive_s * mood_negative_s + ema_beep +      Sex + temp_slope_z + temp_mean_z + acc_delta + physical_excercise_dur +  
    (1 + mood_positive_s * mood_negative_s | castor_record_id) +      (0 + ema_beep | castor_record_id) + (0 + temp_slope_z | castor_record_id) +  
    (0 + temp_mean_z | castor_record_id) + (0 + acc_delta | castor_record_id) +      (0 + physical_excercise_dur | castor_record_id)
   Data: EMA_Data
Control: glmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 14741.2  14910.0  -7344.6  14689.2     4845 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.4581 -0.6350 -0.2565  0.3914  6.9950 

Random effects:
 Groups             Name                            Variance Std.Dev. Corr             
 castor_record_id   (Intercept)                     0.350643 0.59215                   
                    mood_positive_s                 0.007978 0.08932  -0.70            
                    mood_negative_s                 0.022776 0.15092  -0.40  0.59      
                    mood_positive_s:mood_negative_s 0.001555 0.03943  -0.03 -0.52 -0.72
 castor_record_id.1 ema_beep                        0.004044 0.06360                   
 castor_record_id.2 temp_slope_z                    0.032105 0.17918                   
 castor_record_id.3 temp_mean_z                     0.058193 0.24123                   
 castor_record_id.4 acc_delta                       0.005839 0.07642                   
 castor_record_id.5 physical_excercise_dur          0.210590 0.45890                   
 Residual                                           0.345717 0.58798                   
Number of obs: 4871, groups:  castor_record_id, 82

Fixed effects:
                                 Estimate Std. Error t value Pr(>|z|)    
(Intercept)                      1.052598   0.200174   5.258 1.45e-07 ***
mood_positive_s                  0.042101   0.028490   1.478  0.13948    
mood_negative_s                  0.064857   0.050329   1.289  0.19752    
ema_beep                         0.005401   0.012700   0.425  0.67065    
SexMale                          0.176571   0.101192   1.745  0.08100 .  
temp_slope_z                     0.130446   0.034084   3.827  0.00013 ***
temp_mean_z                      0.220188   0.036426   6.045 1.50e-09 ***
acc_delta                        0.208540   0.010920  19.097  < 2e-16 ***
physical_excercise_dur           0.194629   0.138589   1.404  0.16021    
mood_positive_s:mood_negative_s -0.009994   0.009407  -1.062  0.28806    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) md_ps_ md_ng_ ema_bp SexMal tmp_s_ tmp_m_ acc_dl phys__
mood_pstv_s -0.877                                                        
mood_ngtv_s -0.739  0.812                                                 
ema_beep    -0.086 -0.076 -0.049                                          
SexMale     -0.174 -0.024  0.002 -0.014                                   
temp_slop_z -0.008  0.007  0.002 -0.026 -0.008                            
temp_mean_z  0.030 -0.016 -0.005 -0.100 -0.017  0.022                     
acc_delta   -0.053 -0.023 -0.013  0.049 -0.023  0.046  0.049              
physcl_xcr_  0.023 -0.060 -0.031 -0.010  0.013 -0.004  0.016 -0.003       
md_pstv_:__  0.497 -0.723 -0.873  0.040  0.023 -0.004  0.001  0.014  0.031
convergence code: 0
failure to converge in 10000 evaluations

Phasic Magnitude

# Model
glmer.sc_ph_mag_mood <- glmer(sc_phasic_mag_s ~ mood_positive_s*mood_negative_s + 
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex + temp_slope_z + temp_mean_z + 
    acc_delta + physical_excercise_dur +
    (1+mood_positive_s*mood_negative_s| castor_record_id)  + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
  family=Gamma(link="identity"),
    control=glmerControl(calc.derivs = FALSE) )
failure to converge in 10000 evaluations
# Summary
summary(glmer.sc_ph_mag_mood)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( identity )
Formula: sc_phasic_mag_s ~ mood_positive_s * mood_negative_s + ema_beep +      Sex + temp_slope_z + temp_mean_z + acc_delta + physical_excercise_dur +  
    (1 + mood_positive_s * mood_negative_s | castor_record_id) +      (0 + ema_beep | castor_record_id) + (0 + temp_slope_z | castor_record_id) +  
    (0 + temp_mean_z | castor_record_id) + (0 + acc_delta | castor_record_id) +      (0 + physical_excercise_dur | castor_record_id)
   Data: EMA_Data
Control: glmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 11913.3  12082.1  -5930.7  11861.3     4845 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.8368 -0.6324 -0.1321  0.4525  8.7888 

Random effects:
 Groups             Name                            Variance Std.Dev. Corr             
 castor_record_id   (Intercept)                     0.244456 0.49443                   
                    mood_positive_s                 0.003084 0.05554  -0.35            
                    mood_negative_s                 0.001438 0.03792   0.50  0.35      
                    mood_positive_s:mood_negative_s 0.001058 0.03253  -0.61 -0.37 -0.89
 castor_record_id.1 ema_beep                        0.001722 0.04150                   
 castor_record_id.2 temp_slope_z                    0.009954 0.09977                   
 castor_record_id.3 temp_mean_z                     0.021382 0.14623                   
 castor_record_id.4 acc_delta                       0.001572 0.03965                   
 castor_record_id.5 physical_excercise_dur          0.350216 0.59179                   
 Residual                                           0.166456 0.40799                   
Number of obs: 4871, groups:  castor_record_id, 82

Fixed effects:
                                 Estimate Std. Error t value Pr(>|z|)    
(Intercept)                      1.552438   0.146466  10.599  < 2e-16 ***
mood_positive_s                  0.047509   0.019803   2.399  0.01643 *  
mood_negative_s                  0.053930   0.031767   1.698  0.08957 .  
ema_beep                        -0.004206   0.008899  -0.473  0.63646    
SexMale                          0.009777   0.078192   0.125  0.90050    
temp_slope_z                     0.070125   0.021517   3.259  0.00112 ** 
temp_mean_z                      0.130808   0.023914   5.470  4.5e-08 ***
acc_delta                        0.105776   0.005990  17.660  < 2e-16 ***
physical_excercise_dur           0.323006   0.121028   2.669  0.00761 ** 
mood_positive_s:mood_negative_s -0.013569   0.006703  -2.024  0.04294 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) md_ps_ md_ng_ ema_bp SexMal tmp_s_ tmp_m_ acc_dl phys__
mood_pstv_s -0.825                                                        
mood_ngtv_s -0.694  0.811                                                 
ema_beep    -0.100 -0.072 -0.043                                          
SexMale     -0.211 -0.011  0.020 -0.001                                   
temp_slop_z -0.017  0.012  0.013 -0.019 -0.004                            
temp_mean_z  0.028 -0.016 -0.004 -0.109 -0.018  0.036                     
acc_delta   -0.061 -0.023 -0.011  0.056 -0.012  0.064  0.066              
physcl_xcr_  0.013 -0.048 -0.023 -0.007  0.006  0.001  0.018 -0.003       
md_pstv_:__  0.324 -0.670 -0.814  0.033  0.018 -0.012  0.000  0.014  0.023
convergence code: 0
failure to converge in 10000 evaluations

Phasic AUC

# Model
glmer.sc_ph_auc_mood <- glmer(sc_phasic_auc_s ~ mood_positive_s*mood_negative_s + 
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex + temp_slope_z + temp_mean_z + 
    acc_delta + physical_excercise_dur +
    (1+mood_positive_s*mood_negative_s| castor_record_id)  +
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="log"),
    control=glmerControl(calc.derivs = FALSE) )
# Summary
summary(glmer.sc_ph_auc_mood)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( log )
Formula: sc_phasic_auc_s ~ mood_positive_s * mood_negative_s + ema_beep +      Sex + temp_slope_z + temp_mean_z + acc_delta + physical_excercise_dur +  
    (1 + mood_positive_s * mood_negative_s | castor_record_id) +      (0 + ema_beep | castor_record_id) + (0 + temp_slope_z | castor_record_id) +  
    (0 + temp_mean_z | castor_record_id) + (0 + acc_delta | castor_record_id) +      (0 + physical_excercise_dur | castor_record_id)
   Data: EMA_Data
Control: glmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 10443.9  10612.7  -5195.9  10391.9     4845 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.7404 -0.5545 -0.2722  0.1561  7.3519 

Random effects:
 Groups             Name                            Variance  Std.Dev. Corr             
 castor_record_id   (Intercept)                     0.3289788 0.57357                   
                    mood_positive_s                 0.0056379 0.07509  -0.91            
                    mood_negative_s                 0.0146068 0.12086  -0.79  0.88      
                    mood_positive_s:mood_negative_s 0.0005925 0.02434   0.45 -0.71 -0.85
 castor_record_id.1 ema_beep                        0.0008483 0.02913                   
 castor_record_id.2 temp_slope_z                    0.0073684 0.08584                   
 castor_record_id.3 temp_mean_z                     0.0123953 0.11133                   
 castor_record_id.4 acc_delta                       0.0004188 0.02047                   
 castor_record_id.5 physical_excercise_dur          0.0863063 0.29378                   
 Residual                                           0.2430242 0.49297                   
Number of obs: 4871, groups:  castor_record_id, 82

Fixed effects:
                                 Estimate Std. Error t value Pr(>|z|)    
(Intercept)                      0.243959   0.105105   2.321 0.020281 *  
mood_positive_s                  0.010266   0.014198   0.723 0.469668    
mood_negative_s                  0.006440   0.024432   0.264 0.792089    
ema_beep                        -0.004651   0.005552  -0.838 0.402168    
SexMale                          0.034131   0.045364   0.752 0.451820    
temp_slope_z                     0.052555   0.014331   3.667 0.000245 ***
temp_mean_z                      0.089744   0.016284   5.511 3.56e-08 ***
acc_delta                        0.046783   0.002903  16.116  < 2e-16 ***
physical_excercise_dur           0.067156   0.064732   1.037 0.299526    
mood_positive_s:mood_negative_s -0.002741   0.004481  -0.612 0.540729    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) md_ps_ md_ng_ ema_bp SexMal tmp_s_ tmp_m_ acc_dl phys__
mood_pstv_s -0.903                                                        
mood_ngtv_s -0.773  0.848                                                 
ema_beep    -0.075 -0.057 -0.038                                          
SexMale     -0.182  0.000  0.025  0.008                                   
temp_slop_z -0.014  0.006  0.009 -0.011 -0.005                            
temp_mean_z  0.015 -0.010  0.000 -0.089 -0.019  0.034                     
acc_delta   -0.047 -0.013 -0.004  0.040 -0.004  0.067  0.069              
physcl_xcr_  0.007 -0.038 -0.017 -0.005  0.010  0.003  0.015 -0.001       
md_pstv_:__  0.532 -0.736 -0.891  0.034  0.006 -0.007 -0.002  0.007  0.021

Table: Sc vs Mood

Now we make a table, without the FDR correction. This we do later with the full modles in the table.

tab_model(glmer.sc_ton_mood, glmer.sc_phnum_mood, glmer.sc_ph_mag_mood, glmer.sc_ph_auc_mood, 
          dv.labels=c("Tonic", "Number", "Magnitude", "AUC"), 
          title="Table X. SCR and Mood",
            transform=NULL,
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
Table X. SCR and Mood
  Tonic Number Magnitude AUC
Predictors Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p
(Intercept) 0.04 0.04 -0.05 – 0.13 0.90 0.366 1.05 0.20 0.66 – 1.44 5.26 <0.001 1.55 0.15 1.27 – 1.84 10.60 <0.001 0.24 0.11 0.04 – 0.45 2.32 0.020
mood_positive_s 0.00 0.01 -0.01 – 0.02 0.66 0.510 0.04 0.03 -0.01 – 0.10 1.48 0.139 0.05 0.02 0.01 – 0.09 2.40 0.016 0.01 0.01 -0.02 – 0.04 0.72 0.470
mood_negative_s -0.01 0.01 -0.03 – 0.02 -0.44 0.660 0.06 0.05 -0.03 – 0.16 1.29 0.198 0.05 0.03 -0.01 – 0.12 1.70 0.090 0.01 0.02 -0.04 – 0.05 0.26 0.792
ema_beep 0.00 0.00 -0.00 – 0.01 0.69 0.487 0.01 0.01 -0.02 – 0.03 0.43 0.671 -0.00 0.01 -0.02 – 0.01 -0.47 0.636 -0.00 0.01 -0.02 – 0.01 -0.84 0.402
Sex [Male] -0.02 0.02 -0.05 – 0.02 -0.79 0.430 0.18 0.10 -0.02 – 0.37 1.74 0.081 0.01 0.08 -0.14 – 0.16 0.13 0.900 0.03 0.05 -0.05 – 0.12 0.75 0.452
temp_slope_z 0.03 0.01 0.01 – 0.05 3.22 0.001 0.13 0.03 0.06 – 0.20 3.83 <0.001 0.07 0.02 0.03 – 0.11 3.26 0.001 0.05 0.01 0.02 – 0.08 3.67 <0.001
temp_mean_z 0.04 0.01 0.03 – 0.06 4.70 <0.001 0.22 0.04 0.15 – 0.29 6.04 <0.001 0.13 0.02 0.08 – 0.18 5.47 <0.001 0.09 0.02 0.06 – 0.12 5.51 <0.001
acc_delta 0.02 0.00 0.01 – 0.02 9.92 <0.001 0.21 0.01 0.19 – 0.23 19.10 <0.001 0.11 0.01 0.09 – 0.12 17.66 <0.001 0.05 0.00 0.04 – 0.05 16.12 <0.001
physical_excercise_dur 0.08 0.05 -0.01 – 0.17 1.65 0.099 0.19 0.14 -0.08 – 0.47 1.40 0.160 0.32 0.12 0.09 – 0.56 2.67 0.008 0.07 0.06 -0.06 – 0.19 1.04 0.300
mood_positive_s *
mood_negative_s
-0.00 0.00 -0.01 – 0.00 -0.33 0.743 -0.01 0.01 -0.03 – 0.01 -1.06 0.288 -0.01 0.01 -0.03 – -0.00 -2.02 0.043 -0.00 0.00 -0.01 – 0.01 -0.61 0.541
Random Effects
σ2 0.08 0.35 0.17 0.24
τ00 0.00 castor_record_id 0.35 castor_record_id 0.24 castor_record_id 0.33 castor_record_id
0.00 castor_record_id.1 0.00 castor_record_id.1 0.00 castor_record_id.1 0.00 castor_record_id.1
0.00 castor_record_id.2 0.03 castor_record_id.2 0.01 castor_record_id.2 0.01 castor_record_id.2
0.00 castor_record_id.3 0.06 castor_record_id.3 0.02 castor_record_id.3 0.01 castor_record_id.3
0.00 castor_record_id.4 0.01 castor_record_id.4 0.00 castor_record_id.4 0.00 castor_record_id.4
0.07 castor_record_id.5 0.21 castor_record_id.5 0.35 castor_record_id.5 0.09 castor_record_id.5
τ11 0.00 castor_record_id.mood_negative_s 0.01 castor_record_id.mood_positive_s 0.00 castor_record_id.mood_positive_s 0.01 castor_record_id.mood_positive_s
0.00 castor_record_id.mood_positive_s:mood_negative_s 0.02 castor_record_id.mood_negative_s 0.00 castor_record_id.mood_negative_s 0.01 castor_record_id.mood_negative_s
  0.00 castor_record_id.mood_positive_s:mood_negative_s 0.00 castor_record_id.mood_positive_s:mood_negative_s 0.00 castor_record_id.mood_positive_s:mood_negative_s
ρ01 0.49 castor_record_id.mood_negative_s -0.70 castor_record_id.mood_positive_s -0.35 castor_record_id.mood_positive_s -0.91 castor_record_id.mood_positive_s
-0.83 castor_record_id.mood_positive_s:mood_negative_s -0.40 castor_record_id.mood_negative_s 0.50 castor_record_id.mood_negative_s -0.79 castor_record_id.mood_negative_s
  -0.03 castor_record_id.mood_positive_s:mood_negative_s -0.61 castor_record_id.mood_positive_s:mood_negative_s 0.45 castor_record_id.mood_positive_s:mood_negative_s
ICC 0.05 0.32 0.41 0.13
N 82 castor_record_id 82 castor_record_id 82 castor_record_id 82 castor_record_id
Observations 4871 4871 4871 4871
Marginal R2 / Conditional R2 0.104 / 0.152 0.678 / 0.780 0.500 / 0.706 0.173 / 0.281

4.3.2 Heart Rate

Mean

glmer.hr_mean_mood <- glmer(hr_mean_s ~ mood_positive_s*mood_negative_s + 
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex + temp_slope_z + temp_mean_z + 
    acc_delta + physical_excercise_dur +
    (1+mood_positive_s*mood_negative_s| castor_record_id)  + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="log"),
    control=glmerControl(calc.derivs = FALSE) )
# Summary
summary(glmer.hr_mean_mood)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( log )
Formula: hr_mean_s ~ mood_positive_s * mood_negative_s + ema_beep + Sex +      temp_slope_z + temp_mean_z + acc_delta + physical_excercise_dur +  
    (1 + mood_positive_s * mood_negative_s | castor_record_id) +      (0 + ema_beep | castor_record_id) + (0 + temp_slope_z | castor_record_id) +  
    (0 + temp_mean_z | castor_record_id) + (0 + acc_delta | castor_record_id) +      (0 + physical_excercise_dur | castor_record_id)
   Data: EMA_Data
Control: glmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
  9058.4   9226.3  -4503.2   9006.4     4685 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.4356 -0.5907 -0.0601  0.5214 10.2865 

Random effects:
 Groups             Name                            Variance  Std.Dev. Corr             
 castor_record_id   (Intercept)                     3.570e-02 0.188932                  
                    mood_positive_s                 5.598e-04 0.023661 -0.90            
                    mood_negative_s                 1.263e-03 0.035535 -0.75  0.82      
                    mood_positive_s:mood_negative_s 4.115e-05 0.006415  0.50 -0.69 -0.86
 castor_record_id.1 ema_beep                        1.250e-04 0.011179                  
 castor_record_id.2 temp_slope_z                    7.579e-04 0.027531                  
 castor_record_id.3 temp_mean_z                     1.872e-03 0.043270                  
 castor_record_id.4 acc_delta                       7.545e-05 0.008686                  
 castor_record_id.5 physical_excercise_dur          1.188e-02 0.109011                  
 Residual                                           3.128e-02 0.176858                  
Number of obs: 4711, groups:  castor_record_id, 82

Fixed effects:
                                 Estimate Std. Error t value Pr(>|z|)    
(Intercept)                      1.117392   0.036654  30.485  < 2e-16 ***
mood_positive_s                  0.012585   0.004853   2.593  0.00952 ** 
mood_negative_s                  0.007865   0.008155   0.964  0.33481    
ema_beep                        -0.016230   0.002060  -7.879 3.30e-15 ***
SexMale                         -0.054053   0.019959  -2.708  0.00676 ** 
temp_slope_z                     0.007640   0.005154   1.482  0.13828    
temp_mean_z                     -0.030468   0.006267  -4.862 1.16e-06 ***
acc_delta                        0.033032   0.001208  27.354  < 2e-16 ***
physical_excercise_dur           0.105793   0.023580   4.487 7.24e-06 ***
mood_positive_s:mood_negative_s -0.001236   0.001430  -0.864  0.38733    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) md_ps_ md_ng_ ema_bp SexMal tmp_s_ tmp_m_ acc_dl phys__
mood_pstv_s -0.889                                                        
mood_ngtv_s -0.753  0.828                                                 
ema_beep    -0.072 -0.068 -0.043                                          
SexMale     -0.215 -0.004  0.017  0.003                                   
temp_slop_z -0.016  0.012  0.012 -0.022 -0.004                            
temp_mean_z  0.019 -0.011 -0.002 -0.099 -0.025  0.048                     
acc_delta   -0.046 -0.017 -0.006  0.046 -0.013  0.057  0.055              
physcl_xcr_  0.008 -0.038 -0.018 -0.008  0.005  0.004  0.019 -0.001       
md_pstv_:__  0.542 -0.733 -0.894  0.043  0.010 -0.013 -0.001  0.010  0.020

Min

glmer.hr_min_mood <- glmer(hr_min_s ~ mood_positive_s*mood_negative_s + 
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex + temp_slope_z + temp_mean_z + 
    acc_delta + physical_excercise_dur +
    (1+mood_positive_s*mood_negative_s| castor_record_id)  + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="log"),
    control=glmerControl(calc.derivs = FALSE) )
# Summary
summary(glmer.hr_min_mood )
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( log )
Formula: hr_min_s ~ mood_positive_s * mood_negative_s + ema_beep + Sex +      temp_slope_z + temp_mean_z + acc_delta + physical_excercise_dur +  
    (1 + mood_positive_s * mood_negative_s | castor_record_id) +      (0 + ema_beep | castor_record_id) + (0 + temp_slope_z | castor_record_id) +  
    (0 + temp_mean_z | castor_record_id) + (0 + acc_delta | castor_record_id) +      (0 + physical_excercise_dur | castor_record_id)
   Data: EMA_Data
Control: glmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 10935.8  11103.7  -5441.9  10883.8     4685 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.0925 -0.6435 -0.0494  0.5448  9.5294 

Random effects:
 Groups             Name                            Variance  Std.Dev. Corr             
 castor_record_id   (Intercept)                     3.516e-02 0.187506                  
                    mood_positive_s                 5.268e-04 0.022952 -0.82            
                    mood_negative_s                 1.410e-03 0.037545 -0.59  0.76      
                    mood_positive_s:mood_negative_s 4.890e-05 0.006993  0.28 -0.63 -0.81
 castor_record_id.1 ema_beep                        1.177e-04 0.010849                  
 castor_record_id.2 temp_slope_z                    1.089e-03 0.033002                  
 castor_record_id.3 temp_mean_z                     2.142e-03 0.046280                  
 castor_record_id.4 acc_delta                       5.494e-05 0.007412                  
 castor_record_id.5 physical_excercise_dur          1.663e-02 0.128948                  
 Residual                                           4.319e-02 0.207821                  
Number of obs: 4711, groups:  castor_record_id, 82

Fixed effects:
                                  Estimate Std. Error t value Pr(>|z|)    
(Intercept)                      1.1862762  0.0405706  29.240  < 2e-16 ***
mood_positive_s                  0.0131687  0.0053708   2.452 0.014210 *  
mood_negative_s                  0.0060687  0.0093739   0.647 0.517367    
ema_beep                        -0.0112667  0.0022710  -4.961 7.01e-07 ***
SexMale                         -0.0865262  0.0232618  -3.720 0.000199 ***
temp_slope_z                     0.0083430  0.0060915   1.370 0.170811    
temp_mean_z                      0.0157470  0.0069500   2.266 0.023466 *  
acc_delta                        0.0221211  0.0011661  18.970  < 2e-16 ***
physical_excercise_dur           0.1031611  0.0277242   3.721 0.000198 ***
mood_positive_s:mood_negative_s -0.0008534  0.0016382  -0.521 0.602399    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) md_ps_ md_ng_ ema_bp SexMal tmp_s_ tmp_m_ acc_dl phys__
mood_pstv_s -0.869                                                        
mood_ngtv_s -0.717  0.813                                                 
ema_beep    -0.081 -0.076 -0.047                                          
SexMale     -0.218 -0.016 -0.006  0.002                                   
temp_slop_z -0.017  0.012  0.011 -0.022 -0.002                            
temp_mean_z  0.022 -0.012 -0.003 -0.110 -0.026  0.048                     
acc_delta   -0.057 -0.021 -0.006  0.058 -0.011  0.068  0.067              
physcl_xcr_  0.009 -0.040 -0.018 -0.008  0.003  0.004  0.020 -0.001       
md_pstv_:__  0.493 -0.724 -0.885  0.046  0.033 -0.012  0.000  0.011  0.020

Max

glmer.hr_max_mood <- glmer(hr_max_s ~ mood_positive_s*mood_negative_s + 
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex + temp_slope_z + temp_mean_z + 
    acc_delta + physical_excercise_dur +
    (1+mood_positive_s*mood_negative_s| castor_record_id)  + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="log"),
    control=glmerControl(calc.derivs = FALSE) )
# Summary
summary(glmer.hr_max_mood )
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: Gamma  ( log )
Formula: hr_max_s ~ mood_positive_s * mood_negative_s + ema_beep + Sex +      temp_slope_z + temp_mean_z + acc_delta + physical_excercise_dur +  
    (1 + mood_positive_s * mood_negative_s | castor_record_id) +      (0 + ema_beep | castor_record_id) + (0 + temp_slope_z | castor_record_id) +  
    (0 + temp_mean_z | castor_record_id) + (0 + acc_delta | castor_record_id) +      (0 + physical_excercise_dur | castor_record_id)
   Data: EMA_Data
Control: glmerControl(calc.derivs = FALSE)

     AIC      BIC   logLik deviance df.resid 
 12385.4  12553.3  -6166.7  12333.4     4685 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.0237 -0.6361 -0.1246  0.5065  7.2837 

Random effects:
 Groups             Name                            Variance  Std.Dev. Corr             
 castor_record_id   (Intercept)                     3.809e-02 0.195169                  
                    mood_positive_s                 7.842e-04 0.028003 -0.96            
                    mood_negative_s                 8.147e-04 0.028543 -0.85  0.84      
                    mood_positive_s:mood_negative_s 2.729e-05 0.005224  0.56 -0.66 -0.81
 castor_record_id.1 ema_beep                        1.442e-04 0.012008                  
 castor_record_id.2 temp_slope_z                    9.113e-04 0.030187                  
 castor_record_id.3 temp_mean_z                     2.359e-03 0.048567                  
 castor_record_id.4 acc_delta                       6.594e-05 0.008121                  
 castor_record_id.5 physical_excercise_dur          2.309e-02 0.151961                  
 Residual                                           5.140e-02 0.226724                  
Number of obs: 4711, groups:  castor_record_id, 82

Fixed effects:
                                 Estimate Std. Error t value Pr(>|z|)    
(Intercept)                      1.210090   0.041917  28.868  < 2e-16 ***
mood_positive_s                  0.012317   0.005875   2.097   0.0360 *  
mood_negative_s                  0.010179   0.008754   1.163   0.2449    
ema_beep                        -0.016554   0.002477  -6.682 2.35e-11 ***
SexMale                          0.030808   0.017140   1.797   0.0723 .  
temp_slope_z                     0.005902   0.006164   0.958   0.3383    
temp_mean_z                     -0.061956   0.007289  -8.500  < 2e-16 ***
acc_delta                        0.033853   0.001269  26.675  < 2e-16 ***
physical_excercise_dur           0.087195   0.031062   2.807   0.0050 ** 
mood_positive_s:mood_negative_s -0.001865   0.001553  -1.201   0.2299    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) md_ps_ md_ng_ ema_bp SexMal tmp_s_ tmp_m_ acc_dl phys__
mood_pstv_s -0.917                                                        
mood_ngtv_s -0.783  0.828                                                 
ema_beep    -0.088 -0.070 -0.049                                          
SexMale     -0.171  0.003  0.038  0.000                                   
temp_slop_z -0.019  0.013  0.015 -0.024 -0.005                            
temp_mean_z  0.030 -0.020 -0.008 -0.104 -0.032  0.052                     
acc_delta   -0.059 -0.019 -0.006  0.058 -0.018  0.070  0.064              
physcl_xcr_  0.008 -0.039 -0.018 -0.008  0.007  0.004  0.022  0.000       
md_pstv_:__  0.566 -0.723 -0.892  0.048 -0.003 -0.016  0.003  0.011  0.020

Table: HR v Mood

Again, we make a table of the heart rate measures without the FDR correction. We apply that later.

tab_model(glmer.hr_mean_mood, glmer.hr_min_mood, glmer.hr_max_mood, 
          dv.labels=c("Mean", "Min", "Max"), 
          title="Table X. Heart rate vs. Mood",
            transform=NULL, 
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
Table X. Heart rate vs. Mood
  Mean Min Max
Predictors Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p
(Intercept) 1.12 0.04 1.05 – 1.19 30.48 <0.001 1.19 0.04 1.11 – 1.27 29.24 <0.001 1.21 0.04 1.13 – 1.29 28.87 <0.001
mood_positive_s 0.01 0.00 0.00 – 0.02 2.59 0.010 0.01 0.01 0.00 – 0.02 2.45 0.014 0.01 0.01 0.00 – 0.02 2.10 0.036
mood_negative_s 0.01 0.01 -0.01 – 0.02 0.96 0.335 0.01 0.01 -0.01 – 0.02 0.65 0.517 0.01 0.01 -0.01 – 0.03 1.16 0.245
ema_beep -0.02 0.00 -0.02 – -0.01 -7.88 <0.001 -0.01 0.00 -0.02 – -0.01 -4.96 <0.001 -0.02 0.00 -0.02 – -0.01 -6.68 <0.001
Sex [Male] -0.05 0.02 -0.09 – -0.01 -2.71 0.007 -0.09 0.02 -0.13 – -0.04 -3.72 <0.001 0.03 0.02 -0.00 – 0.06 1.80 0.072
temp_slope_z 0.01 0.01 -0.00 – 0.02 1.48 0.138 0.01 0.01 -0.00 – 0.02 1.37 0.171 0.01 0.01 -0.01 – 0.02 0.96 0.338
temp_mean_z -0.03 0.01 -0.04 – -0.02 -4.86 <0.001 0.02 0.01 0.00 – 0.03 2.27 0.023 -0.06 0.01 -0.08 – -0.05 -8.50 <0.001
acc_delta 0.03 0.00 0.03 – 0.04 27.35 <0.001 0.02 0.00 0.02 – 0.02 18.97 <0.001 0.03 0.00 0.03 – 0.04 26.68 <0.001
physical_excercise_dur 0.11 0.02 0.06 – 0.15 4.49 <0.001 0.10 0.03 0.05 – 0.16 3.72 <0.001 0.09 0.03 0.03 – 0.15 2.81 0.005
mood_positive_s *
mood_negative_s
-0.00 0.00 -0.00 – 0.00 -0.86 0.387 -0.00 0.00 -0.00 – 0.00 -0.52 0.602 -0.00 0.00 -0.00 – 0.00 -1.20 0.230
Random Effects
σ2 0.03 0.04 0.05
τ00 0.04 castor_record_id 0.04 castor_record_id 0.04 castor_record_id
0.00 castor_record_id.1 0.00 castor_record_id.1 0.00 castor_record_id.1
0.00 castor_record_id.2 0.00 castor_record_id.2 0.00 castor_record_id.2
0.00 castor_record_id.3 0.00 castor_record_id.3 0.00 castor_record_id.3
0.00 castor_record_id.4 0.00 castor_record_id.4 0.00 castor_record_id.4
0.01 castor_record_id.5 0.02 castor_record_id.5 0.02 castor_record_id.5
τ11 0.00 castor_record_id.mood_positive_s 0.00 castor_record_id.mood_positive_s 0.00 castor_record_id.mood_positive_s
0.00 castor_record_id.mood_negative_s 0.00 castor_record_id.mood_negative_s 0.00 castor_record_id.mood_negative_s
0.00 castor_record_id.mood_positive_s:mood_negative_s 0.00 castor_record_id.mood_positive_s:mood_negative_s 0.00 castor_record_id.mood_positive_s:mood_negative_s
ρ01 -0.90 castor_record_id.mood_positive_s -0.82 castor_record_id.mood_positive_s -0.96 castor_record_id.mood_positive_s
-0.75 castor_record_id.mood_negative_s -0.59 castor_record_id.mood_negative_s -0.85 castor_record_id.mood_negative_s
0.50 castor_record_id.mood_positive_s:mood_negative_s 0.28 castor_record_id.mood_positive_s:mood_negative_s 0.56 castor_record_id.mood_positive_s:mood_negative_s
ICC 0.17 0.18 0.07
N 82 castor_record_id 82 castor_record_id 82 castor_record_id
Observations 4711 4711 4711
Marginal R2 / Conditional R2 0.448 / 0.540 0.216 / 0.354 0.387 / 0.427

4.3.3 Table and Plot: Mood and Physiology

Now I can actually print the tables, and the plot along with the FDR correction.

tab_model(glmer.sc_ton_mood, glmer.sc_phnum_mood, glmer.sc_ph_mag_mood, glmer.sc_ph_auc_mood,
                glmer.hr_mean_mood, glmer.hr_min_mood, glmer.hr_max_mood,
          dv.labels=c("SC Tonic", "SC Number", "SC Magnitude", "SC AUC", "HR Mean", "HR Min", "HR Max"), 
          title="Table X. Physio vs. Mood",
            transform=NULL, p.adjust="fdr", 
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
Table X. Physio vs. Mood
  SC Tonic SC Number SC Magnitude SC AUC HR Mean HR Min HR Max
Predictors Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p Estimates std. Error CI Statistic p
(Intercept) 0.04 0.04 -0.05 – 0.13 0.90 0.638 1.05 0.20 0.66 – 1.44 5.26 <0.001 1.55 0.15 1.27 – 1.84 10.60 <0.001 0.24 0.11 0.04 – 0.45 2.32 0.051 1.12 0.04 1.05 – 1.19 30.48 <0.001 1.19 0.04 1.11 – 1.27 29.24 <0.001 1.21 0.04 1.13 – 1.29 28.87 <0.001
mood_positive_s 0.00 0.01 -0.01 – 0.02 0.66 0.638 0.04 0.03 -0.01 – 0.10 1.48 0.229 0.05 0.02 0.01 – 0.09 2.40 0.027 0.01 0.01 -0.02 – 0.04 0.72 0.587 0.01 0.00 0.00 – 0.02 2.59 0.014 0.01 0.01 0.00 – 0.02 2.45 0.024 0.01 0.01 0.00 – 0.02 2.10 0.060
mood_negative_s -0.01 0.01 -0.03 – 0.02 -0.44 0.734 0.06 0.05 -0.03 – 0.16 1.29 0.247 0.05 0.03 -0.01 – 0.12 1.70 0.112 0.01 0.02 -0.04 – 0.05 0.26 0.792 0.01 0.01 -0.01 – 0.02 0.96 0.372 0.01 0.01 -0.01 – 0.02 0.65 0.575 0.01 0.01 -0.01 – 0.03 1.16 0.272
ema_beep 0.00 0.00 -0.00 – 0.01 0.69 0.638 0.01 0.01 -0.02 – 0.03 0.43 0.671 -0.00 0.01 -0.02 – 0.01 -0.47 0.707 -0.00 0.01 -0.02 – 0.01 -0.84 0.587 -0.02 0.00 -0.02 – -0.01 -7.88 <0.001 -0.01 0.00 -0.02 – -0.01 -4.96 <0.001 -0.02 0.00 -0.02 – -0.01 -6.68 <0.001
Sex [Male] -0.02 0.02 -0.05 – 0.02 -0.79 0.638 0.18 0.10 -0.02 – 0.37 1.74 0.162 0.01 0.08 -0.14 – 0.16 0.13 0.900 0.03 0.05 -0.05 – 0.12 0.75 0.587 -0.05 0.02 -0.09 – -0.01 -2.71 0.011 -0.09 0.02 -0.13 – -0.04 -3.72 <0.001 0.03 0.02 -0.00 – 0.06 1.80 0.103
temp_slope_z 0.03 0.01 0.01 – 0.05 3.22 0.004 0.13 0.03 0.06 – 0.20 3.83 <0.001 0.07 0.02 0.03 – 0.11 3.26 0.003 0.05 0.01 0.02 – 0.08 3.67 0.001 0.01 0.01 -0.00 – 0.02 1.48 0.173 0.01 0.01 -0.00 – 0.02 1.37 0.214 0.01 0.01 -0.01 – 0.02 0.96 0.338
temp_mean_z 0.04 0.01 0.03 – 0.06 4.70 <0.001 0.22 0.04 0.15 – 0.29 6.04 <0.001 0.13 0.02 0.08 – 0.18 5.47 <0.001 0.09 0.02 0.06 – 0.12 5.51 <0.001 -0.03 0.01 -0.04 – -0.02 -4.86 <0.001 0.02 0.01 0.00 – 0.03 2.27 0.034 -0.06 0.01 -0.08 – -0.05 -8.50 <0.001
acc_delta 0.02 0.00 0.01 – 0.02 9.92 <0.001 0.21 0.01 0.19 – 0.23 19.10 <0.001 0.11 0.01 0.09 – 0.12 17.66 <0.001 0.05 0.00 0.04 – 0.05 16.12 <0.001 0.03 0.00 0.03 – 0.04 27.35 <0.001 0.02 0.00 0.02 – 0.02 18.97 <0.001 0.03 0.00 0.03 – 0.04 26.68 <0.001
physical_excercise_dur 0.08 0.05 -0.01 – 0.17 1.65 0.249 0.19 0.14 -0.08 – 0.47 1.40 0.229 0.32 0.12 0.09 – 0.56 2.67 0.015 0.07 0.06 -0.06 – 0.19 1.04 0.587 0.11 0.02 0.06 – 0.15 4.49 <0.001 0.10 0.03 0.05 – 0.16 3.72 <0.001 0.09 0.03 0.03 – 0.15 2.81 0.010
mood_positive_s *
mood_negative_s
-0.00 0.00 -0.01 – 0.00 -0.33 0.743 -0.01 0.01 -0.03 – 0.01 -1.06 0.320 -0.01 0.01 -0.03 – -0.00 -2.02 0.061 -0.00 0.00 -0.01 – 0.01 -0.61 0.601 -0.00 0.00 -0.00 – 0.00 -0.86 0.387 -0.00 0.00 -0.00 – 0.00 -0.52 0.602 -0.00 0.00 -0.00 – 0.00 -1.20 0.272
Random Effects
σ2 0.08 0.35 0.17 0.24 0.03 0.04 0.05
τ00 0.00 castor_record_id 0.35 castor_record_id 0.24 castor_record_id 0.33 castor_record_id 0.04 castor_record_id 0.04 castor_record_id 0.04 castor_record_id
0.00 castor_record_id.1 0.00 castor_record_id.1 0.00 castor_record_id.1 0.00 castor_record_id.1 0.00 castor_record_id.1 0.00 castor_record_id.1 0.00 castor_record_id.1
0.00 castor_record_id.2 0.03 castor_record_id.2 0.01 castor_record_id.2 0.01 castor_record_id.2 0.00 castor_record_id.2 0.00 castor_record_id.2 0.00 castor_record_id.2
0.00 castor_record_id.3 0.06 castor_record_id.3 0.02 castor_record_id.3 0.01 castor_record_id.3 0.00 castor_record_id.3 0.00 castor_record_id.3 0.00 castor_record_id.3
0.00 castor_record_id.4 0.01 castor_record_id.4 0.00 castor_record_id.4 0.00 castor_record_id.4 0.00 castor_record_id.4 0.00 castor_record_id.4 0.00 castor_record_id.4
0.07 castor_record_id.5 0.21 castor_record_id.5 0.35 castor_record_id.5 0.09 castor_record_id.5 0.01 castor_record_id.5 0.02 castor_record_id.5 0.02 castor_record_id.5
τ11 0.00 castor_record_id.mood_negative_s 0.01 castor_record_id.mood_positive_s 0.00 castor_record_id.mood_positive_s 0.01 castor_record_id.mood_positive_s 0.00 castor_record_id.mood_positive_s 0.00 castor_record_id.mood_positive_s 0.00 castor_record_id.mood_positive_s
0.00 castor_record_id.mood_positive_s:mood_negative_s 0.02 castor_record_id.mood_negative_s 0.00 castor_record_id.mood_negative_s 0.01 castor_record_id.mood_negative_s 0.00 castor_record_id.mood_negative_s 0.00 castor_record_id.mood_negative_s 0.00 castor_record_id.mood_negative_s
  0.00 castor_record_id.mood_positive_s:mood_negative_s 0.00 castor_record_id.mood_positive_s:mood_negative_s 0.00 castor_record_id.mood_positive_s:mood_negative_s 0.00 castor_record_id.mood_positive_s:mood_negative_s 0.00 castor_record_id.mood_positive_s:mood_negative_s 0.00 castor_record_id.mood_positive_s:mood_negative_s
ρ01 0.49 castor_record_id.mood_negative_s -0.70 castor_record_id.mood_positive_s -0.35 castor_record_id.mood_positive_s -0.91 castor_record_id.mood_positive_s -0.90 castor_record_id.mood_positive_s -0.82 castor_record_id.mood_positive_s -0.96 castor_record_id.mood_positive_s
-0.83 castor_record_id.mood_positive_s:mood_negative_s -0.40 castor_record_id.mood_negative_s 0.50 castor_record_id.mood_negative_s -0.79 castor_record_id.mood_negative_s -0.75 castor_record_id.mood_negative_s -0.59 castor_record_id.mood_negative_s -0.85 castor_record_id.mood_negative_s
  -0.03 castor_record_id.mood_positive_s:mood_negative_s -0.61 castor_record_id.mood_positive_s:mood_negative_s 0.45 castor_record_id.mood_positive_s:mood_negative_s 0.50 castor_record_id.mood_positive_s:mood_negative_s 0.28 castor_record_id.mood_positive_s:mood_negative_s 0.56 castor_record_id.mood_positive_s:mood_negative_s
ICC 0.05 0.32 0.41 0.13 0.17 0.18 0.07
N 82 castor_record_id 82 castor_record_id 82 castor_record_id 82 castor_record_id 82 castor_record_id 82 castor_record_id 82 castor_record_id
Observations 4871 4871 4871 4871 4711 4711 4711
Marginal R2 / Conditional R2 0.104 / 0.152 0.678 / 0.780 0.500 / 0.706 0.173 / 0.281 0.448 / 0.540 0.216 / 0.354 0.387 / 0.427
# Subset variables of interests
plot.physio <- plot_models(glmer.sc_ton_mood, glmer.sc_phnum_mood, glmer.hr_mean_mood)
rm_term <- as.vector(plot.physio$data$term[1:97])
rm_term <- rm_term[rm_term != "mood_positive_s" & rm_term!="mood_negative_s"]
# Set the colours
col_list <-c('#7570B3','#7570B3','#7570B3',"#D95F02", "#D95F02", '#D95F02', '#D95F02', "#1B9E77", "#1B9E77")
# Make the plot
plot.pos_mood_resid <- plot_models( glmer.sc_ton_mood, glmer.sc_phnum_mood, glmer.sc_ph_mag_mood, glmer.sc_ph_auc_mood,
                glmer.hr_mean_mood, glmer.hr_min_mood, glmer.hr_max_mood,
              m.labels=c("SC Tonic", "SC Number", "SC Magnitued", "SC AUC","HR Mean", "HR Minimum", "HR Maximum"),
           axis.labels = c(" "),
            # Stastistical Stuff
           transform=NULL,
            rm.terms = rm_term,
            #show.values = T,
            #value.size = 4, 
            #std.est=T, 
            show.p=T,
            p.shape=T,
            p.adjust = "fdr", 
            legend.pval.title = "Significance", 
            # Visual Stuff
            colors=col_list,
            dot.size=2,
            line.size = 1,
            spacing=0.7, 
            vline.color = "darkgrey", 
            legend.title = "") + 
            ptheme + scale_y_continuous(breaks=c( -0.2, -.1,0, .1,.2)) + 
            theme(axis.ticks.y=element_blank(), 
                  axis.title = element_text(size=16),axis.text.x=element_text(size=11),
                  panel.grid.major.x = element_line(colour = "grey95"),
                  panel.grid.minor.x = element_line(colour = "grey90")) 
Scale for 'y' is already present. Adding another scale for 'y', which will replace the existing scale.
# Plot and Save
plot.pos_mood_resid + coord_flip(ylim=c(-.25,.25)) + theme(panel.grid.major.y = element_line(colour = "grey95"), panel.grid.minor.y = element_line(colour = "grey90"))
Coordinate system already present. Adding new coordinate system, which will replace the existing one.

#ggsave("figures/fig_MoodkResid_ALL.tiff", units="in", width=5, height=5, dpi=300, compression = 'lzw', bg="transparent")

4.4 Mediation anaylsis

In the stress week, we see a decreease in both positive mood and physiology. However, we also see an increase in stress, which we know is related to some physiology (specifically, SC magnitude). So we need to actually confirm that what we see in the stress week (i.e. the physiology arousal decrease) is actually due to the positive mood changes. To this end, we perfrom a mediation analysis. We first need to filter out the nan’s here for some reason though, and we cant really add any covariates in an easy way. So we will stick to the simplest model here.

library(mediation)
set.seed(123)
EMA_Sub <- EMA_Data %>% dplyr::select(castor_record_id, Week_Type, sc_phasic_mag_s, mood_positive_s, event_tot_s) %>% filter(complete.cases(.))

4.4.1 Positive Mood

Now that we have filtered the data, we run the first of the mediation analyses. Here we test whether the effect of week on the SC measures is mediated by positive mood.

# Set up
# Main effect
fit.totaleffect=glmer(sc_phasic_mag_s ~ Week_Type  + (1|castor_record_id), EMA_Sub)
calling glmer() with family=gaussian (identity link) as a shortcut to lmer() is deprecated; please call lmer() directly
summary(fit.totaleffect)
Linear mixed model fit by REML ['lmerMod']
Formula: sc_phasic_mag_s ~ Week_Type + (1 | castor_record_id)
   Data: EMA_Sub

REML criterion at convergence: 14521.3

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.6166 -0.6538 -0.1600  0.3745  6.0787 

Random effects:
 Groups           Name        Variance Std.Dev.
 castor_record_id (Intercept) 0.2098   0.458   
 Residual                     1.1053   1.051   
Number of obs: 4871, groups:  castor_record_id, 82

Fixed effects:
                Estimate Std. Error t value
(Intercept)      2.37842    0.05518  43.105
Week_TypeStress -0.17865    0.03046  -5.865

Correlation of Fixed Effects:
            (Intr)
Wk_TypStrss -0.279
# Mediations
fit.mediator=glmer(mood_positive_s ~ Week_Type  + (1|castor_record_id), EMA_Sub)
calling glmer() with family=gaussian (identity link) as a shortcut to lmer() is deprecated; please call lmer() directly
summary(fit.mediator)
Linear mixed model fit by REML ['lmerMod']
Formula: mood_positive_s ~ Week_Type + (1 | castor_record_id)
   Data: EMA_Sub

REML criterion at convergence: 16551.7

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.6490 -0.6025  0.0561  0.6408  3.7924 

Random effects:
 Groups           Name        Variance Std.Dev.
 castor_record_id (Intercept) 0.9616   0.9806  
 Residual                     1.6479   1.2837  
Number of obs: 4871, groups:  castor_record_id, 82

Fixed effects:
                Estimate Std. Error t value
(Intercept)      6.67833    0.11161   59.83
Week_TypeStress -0.51174    0.03723  -13.75

Correlation of Fixed Effects:
            (Intr)
Wk_TypStrss -0.168
# Combined
fit.dv=glmer(sc_phasic_mag_s ~ Week_Type + mood_positive_s  + (1|castor_record_id), EMA_Sub)
calling glmer() with family=gaussian (identity link) as a shortcut to lmer() is deprecated; please call lmer() directly
summary(fit.dv)
Linear mixed model fit by REML ['lmerMod']
Formula: sc_phasic_mag_s ~ Week_Type + mood_positive_s + (1 | castor_record_id)
   Data: EMA_Sub

REML criterion at convergence: 14522.5

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.6395 -0.6415 -0.1645  0.3849  6.0210 

Random effects:
 Groups           Name        Variance Std.Dev.
 castor_record_id (Intercept) 0.2094   0.4576  
 Residual                     1.1042   1.0508  
Number of obs: 4871, groups:  castor_record_id, 82

Fixed effects:
                Estimate Std. Error t value
(Intercept)      2.19159    0.09483  23.111
Week_TypeStress -0.16440    0.03101  -5.302
mood_positive_s  0.02797    0.01155   2.421

Correlation of Fixed Effects:
            (Intr) Wk_TyS
Wk_TypStrss -0.314       
mood_pstv_s -0.814  0.190
# Mediation analysis
results = mediate(model.m=fit.mediator, model.y=fit.dv, treat='Week_Type', mediator='mood_positive_s', boot=F, sims=5000)
treatment and control values do not match factor levels; using Control and Stress as control and treatment, respectively
summary(results)

Causal Mediation Analysis 

Quasi-Bayesian Confidence Intervals

Mediator Groups: castor_record_id 

Outcome Groups: castor_record_id 

Output Based on Overall Averages Across Groups 

                         Estimate 95% CI Lower 95% CI Upper p-value    
ACME (control)            -0.0144      -0.0263         0.00   0.012 *  
ACME (treated)            -0.0144      -0.0263         0.00   0.012 *  
ADE (control)             -0.1642      -0.2234        -0.10  <2e-16 ***
ADE (treated)             -0.1642      -0.2234        -0.10  <2e-16 ***
Total Effect              -0.1786      -0.2367        -0.12  <2e-16 ***
Prop. Mediated (control)   0.0796       0.0169         0.17   0.012 *  
Prop. Mediated (treated)   0.0796       0.0169         0.17   0.012 *  
ACME (average)            -0.0144      -0.0263         0.00   0.012 *  
ADE (average)             -0.1642      -0.2234        -0.10  <2e-16 ***
Prop. Mediated (average)   0.0796       0.0169         0.17   0.012 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Sample Size Used: 4871 


Simulations: 5000 

The results show that indeed, the results are mediated by positive mood.

4.4.2 Event Stress

We now need to refit the models and check whether event stress is doing any supression or mediation. So we run another model to check that.

# Main effect
fit.totaleffect=glmer(sc_phasic_mag_s ~ Week_Type  + (1|castor_record_id), EMA_Sub)
calling glmer() with family=gaussian (identity link) as a shortcut to lmer() is deprecated; please call lmer() directly
summary(fit.totaleffect)
Linear mixed model fit by REML ['lmerMod']
Formula: sc_phasic_mag_s ~ Week_Type + (1 | castor_record_id)
   Data: EMA_Sub

REML criterion at convergence: 14521.3

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.6166 -0.6538 -0.1600  0.3745  6.0787 

Random effects:
 Groups           Name        Variance Std.Dev.
 castor_record_id (Intercept) 0.2098   0.458   
 Residual                     1.1053   1.051   
Number of obs: 4871, groups:  castor_record_id, 82

Fixed effects:
                Estimate Std. Error t value
(Intercept)      2.37842    0.05518  43.105
Week_TypeStress -0.17865    0.03046  -5.865

Correlation of Fixed Effects:
            (Intr)
Wk_TypStrss -0.279
# Mediations
fit.mediator=glmer(event_tot_s ~ Week_Type  + (1|castor_record_id), EMA_Sub)
calling glmer() with family=gaussian (identity link) as a shortcut to lmer() is deprecated; please call lmer() directly
summary(fit.mediator)
Linear mixed model fit by REML ['lmerMod']
Formula: event_tot_s ~ Week_Type + (1 | castor_record_id)
   Data: EMA_Sub

REML criterion at convergence: 15902.1

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.9369 -0.6062  0.0213  0.6250  4.1070 

Random effects:
 Groups           Name        Variance Std.Dev.
 castor_record_id (Intercept) 0.1397   0.3738  
 Residual                     1.4829   1.2177  
Number of obs: 4871, groups:  castor_record_id, 82

Fixed effects:
                Estimate Std. Error t value
(Intercept)      5.47163    0.04848 112.866
Week_TypeStress  0.32736    0.03524   9.289

Correlation of Fixed Effects:
            (Intr)
Wk_TypStrss -0.368
# Combined
fit.dv=glmer(sc_phasic_mag_s ~ Week_Type + event_tot_s   + (1|castor_record_id), EMA_Sub)
calling glmer() with family=gaussian (identity link) as a shortcut to lmer() is deprecated; please call lmer() directly
summary(fit.dv)
Linear mixed model fit by REML ['lmerMod']
Formula: sc_phasic_mag_s ~ Week_Type + event_tot_s + (1 | castor_record_id)
   Data: EMA_Sub

REML criterion at convergence: 14527.9

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.6252 -0.6550 -0.1594  0.3737  6.0909 

Random effects:
 Groups           Name        Variance Std.Dev.
 castor_record_id (Intercept) 0.2097   0.4579  
 Residual                     1.1055   1.0514  
Number of obs: 4871, groups:  castor_record_id, 82

Fixed effects:
                 Estimate Std. Error t value
(Intercept)      2.340709   0.087530  26.742
Week_TypeStress -0.180920   0.030734  -5.887
event_tot_s      0.006892   0.012422   0.555

Correlation of Fixed Effects:
            (Intr) Wk_TyS
Wk_TypStrss -0.071       
event_tot_s -0.776 -0.133
# Mediation analysis
results2 = mediate(model.m=fit.mediator, model.y=fit.dv, treat='Week_Type', mediator='event_tot_s', boot=F, sims=5000)
treatment and control values do not match factor levels; using Control and Stress as control and treatment, respectively
summary(results2)

Causal Mediation Analysis 

Quasi-Bayesian Confidence Intervals

Mediator Groups: castor_record_id 

Outcome Groups: castor_record_id 

Output Based on Overall Averages Across Groups 

                         Estimate 95% CI Lower 95% CI Upper p-value    
ACME (control)            0.00228     -0.00563         0.01    0.58    
ACME (treated)            0.00228     -0.00563         0.01    0.58    
ADE (control)            -0.18031     -0.23996        -0.12  <2e-16 ***
ADE (treated)            -0.18031     -0.23996        -0.12  <2e-16 ***
Total Effect             -0.17803     -0.23750        -0.12  <2e-16 ***
Prop. Mediated (control) -0.01238     -0.06363         0.03    0.58    
Prop. Mediated (treated) -0.01238     -0.06363         0.03    0.58    
ACME (average)            0.00228     -0.00563         0.01    0.58    
ADE (average)            -0.18031     -0.23996        -0.12  <2e-16 ***
Prop. Mediated (average) -0.01238     -0.06363         0.03    0.58    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Sample Size Used: 4871 


Simulations: 5000 

Here, we see that indeed there is no mediation

5 Random Forests

We were able to establish that physiology and mood both change in the weeks under chronic stress. That is good, because now we can see how well we can use this informaiton in predictive models. To this end, we use the randomForest package plus some extra functions to test our prediction. Firrst lets set a seed and load a packacge for these analyses.

library(randomForest)
set.seed(123)

5.1 OOB Error

Before going into the details of the models, we first subset the data to omit any nans. We then check the out of back error for random forest models predicting week from the data types. We run three models predicting week type from each of the following:

  1. Affect
  2. Physiology
  3. Combination

After checking the OOB errors, we can split the data into the training/testing sets.

# Variables for Forest
vars.forest <- c( "Week_Type", "mood_positive", "mood_negative", "sc_tonic_mean", "sc_phasic_mag", "sc_phasic_dur", "sc_phasic_auc", "sc_phasic_num","hr_mean", "hr_max", "hr_min", "hr_sd", "acc_delta", "temp_mean")
vars.forest.physio <-c( "sc_tonic_mean", "sc_phasic_mag", "sc_phasic_dur", "sc_phasic_auc", "sc_phasic_num","hr_mean", "hr_max", "hr_min", "hr_sd", "Week_Type" )
# Subset the data
df.RandomForest <- EMA_Data[,vars.forest]
df.RandomForest <- na.omit(df.RandomForest)
df.RandomForest.physio <- df.RandomForest[,vars.forest.physio]

Mood

This modle classifies week type from the affect items

# Run random forest model for mood vars
forest.mood <- randomForest(Week_Type ~ mood_positive + mood_negative,
                            data=df.RandomForest, 
                            ntree=5000,
                          importance = TRUE)
forest.mood

Call:
 randomForest(formula = Week_Type ~ mood_positive + mood_negative,      data = df.RandomForest, ntree = 5000, importance = TRUE) 
               Type of random forest: classification
                     Number of trees: 5000
No. of variables tried at each split: 1

        OOB estimate of  error rate: 43.45%
Confusion matrix:
        Control Stress class.error
Control    1397    824   0.3710041
Stress     1128   1144   0.4964789

Physio

Now we can check what the physio data looks like. The OOB is 38.43 for the mood data. Can we do better with the full data? And what is the most important variable in these models?

# Run random forest full model
vars.forest.physio <- c( "sc_tonic_mean", "sc_phasic_mag", "sc_phasic_dur", "sc_phasic_auc", "sc_phasic_num","hr_mean", "hr_max", "hr_min", "hr_sd", "acc_delta", "temp_mean")
forest.full <- randomForest( as.formula(paste("Week_Type", "~", (paste(vars.forest.physio, collapse="+")))) ,
                            data=df.RandomForest, 
                            ntree=5000,
                            importance = TRUE)
forest.full

Call:
 randomForest(formula = as.formula(paste("Week_Type", "~", (paste(vars.forest.physio,      collapse = "+")))), data = df.RandomForest, ntree = 5000,      importance = TRUE) 
               Type of random forest: classification
                     Number of trees: 5000
No. of variables tried at each split: 3

        OOB estimate of  error rate: 45.36%
Confusion matrix:
        Control Stress class.error
Control    1156   1065   0.4795137
Stress      973   1299   0.4282570
randomForest::importance(forest.full)
                  Control    Stress MeanDecreaseAccuracy MeanDecreaseGini
sc_tonic_mean  -8.9853097 21.631419            12.072315         237.7048
sc_phasic_mag -11.1918958 20.421922             9.939339         174.0730
sc_phasic_dur  22.8649025 -9.571561            19.010894         104.3321
sc_phasic_auc   0.7914564 13.632900            20.724970         229.0421
sc_phasic_num  10.8494712  4.837696            22.724805         124.5621
hr_mean         2.0238012  8.829096            12.024067         224.0586
hr_max         -2.3256789 16.142368            15.600133         225.0406
hr_min        -15.8804828 30.525435            14.546899         222.8330
hr_sd          -3.6938560 12.473994             8.642465         220.1086
acc_delta      21.6679819 -6.470493            13.461728         239.2759
temp_mean      -1.1658008 18.136056            12.441982         242.1378

Full

Next up I will select the all variables and see if it improves our model.

# Run the forest with most important features
forest.important <- randomForest(Week_Type ~ .,
                            data=df.RandomForest, 
                            ntree=5000,
                            importance = TRUE)
forest.important

Call:
 randomForest(formula = Week_Type ~ ., data = df.RandomForest,      ntree = 5000, importance = TRUE) 
               Type of random forest: classification
                     Number of trees: 5000
No. of variables tried at each split: 3

        OOB estimate of  error rate: 41.09%
Confusion matrix:
        Control Stress class.error
Control    1250    971   0.4371905
Stress      875   1397   0.3851232

Ok so first I looked at the random forest models as a whole without really doing any type of validation of the predictions. We can see that if we look at the mood, we get better predictions for stress and control weeks than looking at the whole set of physio parameters. Thats interesting, but unsurprising. We now need to do some testing and validation.

5.2 LOBO

In order to the validation, we try out a leave-one-beep-out (LOBO) analysis. This analysis will run a random forest model for each subject separately, leaving out one survey when running the model. We then test the model on the beep that was left out. We repeat this process for the subject until we’ve removed each survey/beep out once. This results in a series of predictions that give us an error level for each subject. In order to do this, we have developed a function that is provided in this github directory.

Model 1: Mood

Model

We first run the LOBO model using the custom function.

# Then with the full model
vars.forest.mood <-  c("mood_positive_c", "mood_negative_c")
forest.lobo.mood <- rf.lobo(Data=EMA_Data,
                              SubNr="castor_record_id",
                           xvars=vars.forest.mood,
                              yvar="Week_Type",
                              NoTree=5000)
[1] 0% complete
[1] 10% complete
[1] 20% complete
[1] 30% complete
[1] 40% complete
[1] 50% complete
[1] 60% complete
[1] 70% complete
[1] 80% complete
[1] 90% complete
[1] 100% Complete
as.data.frame(forest.lobo.mood$total$subject_errors)
psych::describe(forest.lobo.mood$total$subject_errors)

Bootstrap

We see we get an estimated error of around 33% for this model. Thats cool. Now we need to test it against the random error. One can assume in theory that the prediction error for a dichotomous variable is 50/50, but we dont like to do things the easy way. Instead, we will do 10000 iterations where we bootstrap resample the stress and control weeks. This will give us the real error rate with a sampling distribution. This was made into a function, but for some reason I couldnt get the function to run in parallel. So instead I run the parallel processing of the bootstrap outside of a function. Its not pretty, but it works.

# BootstrapLOBO.
# { cl <- makeCluster(NoCores-1)
# registerDoSNOW(cl)
# iterations <- 10000
# print("Running, this will take a while...", quote=F)
# pb <- txtProgressBar(max = iterations, style = 3)
# progress <- function(n) setTxtProgressBar(pb, n)
# opts <- list(progress = progress)
# forest.boot.mood <- foreach(i=1:iterations, .options.snow = opts ) %dopar% {
#     rf.BootstrapError(Data=EMA_Data,
#                           Shuffle="Week_Type",
#                           Iterations=1,
#                           SubjectId="castor_record_id",
#                           xvar=vars.forest.mood,
#                           yvar="Week_Type",
#                           Trees=500)
# }
# print("Done!", quote=F)
# stopCluster(cl)
# # Now merge them into one dataframe
# pb <- txtProgressBar(max =length(forest.boot.mood), style = 3)
# forest.boot.mood.merge <- as.data.frame(forest.boot.mood[[1]][2])
# for (i in 2:length(forest.boot.mood)) {
#     setTxtProgressBar(pb, i)
#     df.2merge <- as.data.frame(forest.boot.mood[[i]][2])
#     forest.boot.mood.merge <- merge (df.2merge, forest.boot.mood.merge , by="DataFrame.id")
# }
# # After merging the results into a single data frame, lets also everage the error rate
# forest.boot.mood.merge$averageError <- rowMeans(forest.boot.mood.merge [, -which(names( forest.boot.mood.merge) %in% c("DataFrame.id"))], na.rm=T)
# saveRDS(forest.boot.mood.merge, file = "data/bootstrap_mood.rds")
# }

Now that we have run the bootstrap, we also save it just in case, and then we get the average error, and calcualte the true SD and SE from the sampling distribution.

# Print the Errors
boot.mood.descr <- psych::describe(forest.boot.mood.merge$averageError)
# Also get the true SD of bootstraps
boot.mood.descr$sd <- mean((psych::describe(forest.boot.mood.merge))$sd, na.rm=T)
NAs introduced by coercionno non-missing arguments to min; returning Infno non-missing arguments to max; returning -Inf
boot.mood.descr$se <- mean((psych::describe(forest.boot.mood.merge))$se, na.rm=T)
NAs introduced by coercionno non-missing arguments to min; returning Infno non-missing arguments to max; returning -Inf
boot.mood.descr

Stouffer’s Test

I will now test the LOBO model using Mood against the bootstrapped LOBO model with the same variables. I made a function to do this. The finction will first calculate a z-score for each subject based on the distribution of the bootstrapped models, then it will calculate the P-value from the z-score. Finally the function sums the z-scores using the stouffer method. Using this method, we see the LOBO models perfrom significantly better than chance. Yay! So within-subject approach works super well!

lobo.mood_null <- rf.null_test(forest.lobo.mood, forest.boot.mood.merge, model_type="LOBO", method="actual")
Loading required package: poolr
lobo.mood_null
$p_val
 [1] 0.1597 0.0197 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
[23] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
[45] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
[67] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000     NA

$combined
combined p-values with:      Stouffer's method
number of p-values combined: 82 
test statistic:              33.193 ~ N(0,1) 
adjustment:                  none 
combined p-value:            <2e-16 

Model 2: Physio

The second model I will test is whether we can predict week type from the physiology data alone. For this, I run the model first to get the LOBO error rate.

Model

We see that it does a bit worse than model 1. But we still need to check the bootstrap error for the model with the physio data. It should be similar to that of the mood though.

# Then with the full model
vars.forest.physio <-  c("sc_tonic_mean", "sc_phasic_mag", "sc_phasic_dur", "sc_phasic_auc", "sc_phasic_num","hr_mean", "hr_max", "hr_min", "hr_sd", "acc_delta", "temp_mean")
forest.lobo.physio <- rf.lobo(Data=EMA_Data,
                              SubNr="castor_record_id",
                              xvars=vars.forest.physio,
                              yvar="Week_Type",
                              NoTree=5000)
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Use `NA` as row index to obtain a row full of `NA` values.
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Call `lifecycle::last_warnings()` to see where this warning was generated.The `i` argument of ``[.tbl_df`()` must lie in [-rows, 0] if negative, as of tibble 3.0.0.
Use `NA` as row index to obtain a row full of `NA` values.
This warning is displayed once every 8 hours.
Call `lifecycle::last_warnings()` to see where this warning was generated.
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as.data.frame(forest.lobo.physio$total$subject_errors)
psych::describe(forest.lobo.physio$total$subject_errors)

Bootstrap

We again do the bootstrap model, and then save it as an object for later use.

# # LOBO Bootstrapping
# { cl <- makeCluster(NoCores-1)
#     registerDoSNOW(cl)
#     iterations <- 10000
#     print("Running, this will take a while...", quote=F)
#     pb <- txtProgressBar(max = iterations, style = 3)
#     progress <- function(n) setTxtProgressBar(pb, n)
#     opts <- list(progress = progress)
#     forest.boot.physio <- foreach(i=1:iterations, .options.snow = opts ) %dopar% {
#         rf.BootstrapError(Data=EMA_Data,
#                                           Shuffle="Week_Type",
#                                           Iterations=1,
#                                           SubjectId="castor_record_id",
#                                           xvar=vars.forest.physio,
#                                           yvar="Week_Type",
#                                           Trees=500)
#     }
#     print("Done!", quote=F)
#     stopCluster(cl)
#     
#     # Now merge them into one dataframe
#     pb <- txtProgressBar(max =length(forest.boot.physio), style = 3)
#     forest.boot.physio.merge <- as.data.frame(forest.boot.physio[[1]][2])
#     for (i in 2:length(forest.boot.physio)) {
#         setTxtProgressBar(pb, i)
#         df.2merge <- as.data.frame(forest.boot.physio[[i]][2])
#         forest.boot.physio.merge <- merge(df.2merge, forest.boot.physio.merge , by="DataFrame.id",
#                                           suffixes=c((paste(i,".x")),(paste(i,".y"))))
#     }
#     # Merge it to mean
#     forest.boot.physio.merge$averageError <- rowMeans(forest.boot.physio.merge [, -which(names( forest.boot.physio.merge) %in% c("DataFrame.id"))], na.rm=T)
#     saveRDS( forest.boot.physio.merge, file = "data/bootstrap_physio.rds")
# }

We now calculate the bootstrap SE and SD

# Print the Errors
boot.physio.descr <- psych::describe(forest.boot.physio.merge$averageError)
# Also get the true SD of bootstraps
boot.physio.descr$sd <- mean((psych::describe(forest.boot.physio.merge))$sd, na.rm=T)
NAs introduced by coercionno non-missing arguments to min; returning Infno non-missing arguments to max; returning -Inf
boot.physio.descr$se <- mean((psych::describe(forest.boot.physio.merge))$se, na.rm=T)
NAs introduced by coercionno non-missing arguments to min; returning Infno non-missing arguments to max; returning -Inf
boot.physio.descr

Stouffer’s Test

So now that I have the averaged bootstrap error for the physio model, lets check if the LOBO is more than random with a test against the bootstrap estimates.

lobo.physio_null <- rf.null_test(forest.lobo.physio, forest.boot.physio.merge,  model_type="LOBO", method="actual")
lobo.physio_null
$p_val
 [1] 0.5632 0.0333 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
[23] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
[45] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
[67] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

$combined
combined p-values with:      Stouffer's method
number of p-values combined: 80 
test statistic:              32.62 ~ N(0,1) 
adjustment:                  none 
combined p-value:            <2e-16 

According to the t-test against the bootstrap error sample, the test is above chance level here too. I will again do a model comparison at the end of the model-testing sections.

Model 3: Full

Finally we check the full model using both physio and mood variables.

Model

# Then with the full model
vars.forest.x <-  c("mood_positive_c", "mood_negative_c", "sc_tonic_mean", "sc_phasic_mag", "sc_phasic_dur", "sc_phasic_auc", "sc_phasic_num","hr_mean", "hr_max", "hr_min", "hr_sd", "temp_mean")
forest.lobo.full <- rf.lobo(Data=EMA_Data,
                              SubNr="castor_record_id",
                              xvars=vars.forest.x,
                              yvar="Week_Type",
                              NoTree=5000)
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as.data.frame(forest.lobo.full$total$subject_errors)
psych::describe(forest.lobo.full$total$subject_errors)

Bootstrap

Then I can check the bootstrap error for the model combined model as done before:

# {cl <- makeCluster(NoCores-1)
# registerDoSNOW(cl)
# iterations <- 10000
# print("Running, this will take a while...", quote=F)
# pb <- txtProgressBar(max = iterations, style = 3)
# progress <- function(n) setTxtProgressBar(pb, n)
# opts <- list(progress = progress)
# forest.boot.combi <- foreach(i=1:iterations, .options.snow = opts ) %dopar% {
#     rf.BootstrapError(Data=EMA_Data,
#                                       Shuffle="Week_Type",
#                                       Iterations=1,
#                                       SubjectId="castor_record_id",
#                                       xvar=vars.forest.x,
#                                       yvar="Week_Type",
#                                       Trees=500)
# }
# print("Done!", quote=F)
# stopCluster(cl)
# 
# # Now merge them into one dataframe
# pb <- txtProgressBar(max =length(forest.boot.combi), style = 3)
# forest.boot.combi.merge <- as.data.frame(forest.boot.physio[[1]][2])
# for (i in 2:length(forest.boot.combi)) {
#     setTxtProgressBar(pb, i)
#     df.2merge <- as.data.frame(forest.boot.combi[[i]][2])
#     forest.boot.combi.merge <- merge(df.2merge, forest.boot.combi.merge , by="DataFrame.id",
#                                       suffixes=c((paste(i,".x")),(paste(i,".y"))))
# }
# # Merge it to mean
# forest.boot.combi.merge$averageError <- rowMeans(forest.boot.combi.merge [, -which(names( forest.boot.combi.merge) %in% c("DataFrame.id"))], na.rm=T)
#  saveRDS( forest.boot.combi.merge, file = "data/bootstrap_combi.rds")
# }

We then again calculate the SE and SD of the models

# Print the Errors
boot.combi.descr <- psych::describe(forest.boot.combi.merge$averageError)
# Also get the true SD of bootstraps
boot.combi.descr$sd <- mean((psych::describe(forest.boot.combi.merge))$sd, na.rm=T)
NAs introduced by coercionno non-missing arguments to min; returning Infno non-missing arguments to max; returning -Inf
boot.combi.descr$se <- mean((psych::describe(forest.boot.combi.merge))$se, na.rm=T)
NAs introduced by coercionno non-missing arguments to min; returning Infno non-missing arguments to max; returning -Inf
boot.combi.descr

Stouffer’s Test

And finally I can test the difference between the full model and the bootstrapped one. So we can see again, that our model only improves slightly with the addition of the physio variables (1%). That doesnt seem great. But we can also guess that within the control week there may be times when people are stressed, and vice versa for the stress week.We will do the null test again.

lobo.combi_null <- rf.null_test(forest.lobo.full, forest.boot.combi.merge, model_type="LOBO", method="actual")
lobo.combi_null
$p_val
 [1] 0.1731 0.0037 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
[23] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
[45] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
[67] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

$combined
combined p-values with:      Stouffer's method
number of p-values combined: 80 
test statistic:              32.837 ~ N(0,1) 
adjustment:                  none 
combined p-value:            <2e-16 

Whats the best LOBO?

Now that we’ve established all our models do better than the bootstrap version, we can also test the models against each other. We first check the lowest performers.

5.2.0.1 Mood vs Physio

We filter the data and have to do a couple of manipulations to do a paired t-test.We see that the mood does significantly better

rf.result.df1 <- as.data.frame(forest.lobo.physio$total$subject_errors)
colnames(rf.result.df1)[1] <- "physio"
rf.result.df1$id <- rownames(rf.result.df1)
rf.result.df2 <- as.data.frame(forest.lobo.mood$total$subject_errors)
colnames(rf.result.df2)[1] <- "mood"
rf.result.df2$id <- rownames(rf.result.df2)
rf.result.merge <- merge(rf.result.df1, rf.result.df2, by="id")
tidy(t.test(x=rf.result.merge$physio, y=rf.result.merge$mood, paired=T))

5.2.0.2 Combi vs Mood

Now I test the mood vs full model. It appears that the full model does a lot better than the one with mood only. So it is safe to say that Model 3 > Model 1 > Model 2

rf.result.df1 <- as.data.frame(forest.lobo.full$total$subject_errors)
colnames(rf.result.df1)[1] <- "full"
rf.result.df1$id <- rownames(rf.result.df1)
rf.result.df2 <- as.data.frame(forest.lobo.mood$total$subject_errors)
colnames(rf.result.df2)[1] <- "mood"
rf.result.df2$id <- rownames(rf.result.df2)
rf.result.merge <- merge(rf.result.df1, rf.result.df2, by="id")
tidy(t.test(x=rf.result.merge$full, y=rf.result.merge$mood, paired=T))

5.3 LOSO

Next up is the standard LOSO. The idea here is that we want to check if we can actually use the data of different participants to predict for a completetly new one. This will remove the enitre EMA data set of a single subject, run the model, then cross validate it with the subject that was left out. I can now run the function below, first with a vector only including the mood items, then the full model:

Model 1: Mood

Model

Our first model looks at the mood ratings predicting which week participants are in. I estimate the LOSO error rates below. The model here doesnt do as well as the model with the lobo. Lets try to use the LOBO null distribution to see if its above chance levels next.

# First with mood items
vars.forest.mood <-  c("mood_positive", "mood_negative")
forest.loso.mood <- rf.loso(Data=EMA_Data, 
                       SubNr="castor_record_id", 
                       xvars=vars.forest.mood,
                       yvar="Week_Type",
                       NoTree=5000)
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as.data.frame(forest.loso.mood$error_rate)
psych::describe(forest.loso.mood$error_rate*100, na.rm=T)

Test

Here I will try to check the LOSO model vs. the null distribution estimated from the bootstrap we did earler. The loso model did not perform better than the bootstrapped estimates.

forest.loso_mood_null <- rf.null_test(forest.loso.mood, forest.boot.mood.merge,  model_type="LOSO", method="actual")
forest.loso_mood_null
$p_val
 [1] 0.3563 0.5799 0.0000 0.7926 0.0000 0.0000 0.0000 0.0000 0.3076 0.8950 0.0012 0.0076 0.8176 0.5599 1.0000 0.0000 0.0177 0.0225 0.0833 0.0000 1.0000 0.0000
[23] 1.0000 0.0000 0.8348 0.7252 1.0000 0.0000 0.9897 0.0000 0.0004 0.0000 0.0000 0.1273 0.0001 0.9952 0.9466 0.0113 0.0000 0.9514 0.2565 0.0000 0.0000 0.0000
[45] 0.9906 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000 0.0022 0.0000 0.6286 0.9995 0.0000 1.0000 0.9948 0.0000 0.0020 1.0000 0.0001 1.0000
[67] 0.0016 0.2036 0.0000 0.0000 1.0000 0.9998 0.6477 1.0000 1.0000 0.0015 1.0000 0.0643 0.0000 0.0282 0.0006 0.0000 1.0000

$combined
combined p-values with:      Stouffer's method
number of p-values combined: 83 
test statistic:              -Inf ~ N(0,1) 
adjustment:                  none 
combined p-value:            1 

Model 2: Physio

The second model is looking at the physio variables predicting week type. We see that it only achieves 47.83% success. We will test this now against the bootstrapped error rate. #### Model{-}

# Then with the full model
vars.forest.physio <-  c("sc_tonic_mean", "sc_phasic_mag", "sc_phasic_dur", "sc_phasic_auc", "sc_phasic_num","hr_mean", "hr_max", "hr_min", "hr_sd", "acc_delta", "temp_mean")
forest.loso.physio <- rf.loso(Data=EMA_Data, 
                       SubNr="castor_record_id", 
                       xvars=vars.forest.physio,
                       yvar="Week_Type",
                       NoTree=5000)
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as.data.frame(forest.loso.physio$error_rate)
psych::describe(forest.loso.physio$error_rate*100)

Test

Next we check the physio variables against the null distribution. Here we see that it its also not signficantly better than chance.

forest.loso_physio_null <- rf.null_test(forest.loso.physio, forest.boot.physio.merge, model_type="LOSO", method="actual")
forest.loso_physio_null
$p_val
 [1] 0.4703 0.8593 0.2199 0.4417 0.8771 0.0782 0.9687 0.4285 0.0932     NA 0.0021 0.1961 0.0539 0.7650 0.2076 0.0000 0.0000 1.0000 0.0000 0.9629 1.0000 0.0000
[23] 0.0000 0.0305 0.0000 0.2412 1.0000 0.3724 0.9777 0.0000 0.0090 1.0000 0.5665 0.0000 0.0073 0.9108 0.5631 0.9988 0.9466 0.0000 0.0006 0.1017 0.0000 0.9665
[45] 0.5722 0.3070 0.0000 1.0000 0.0000 0.0000 1.0000 0.0001 1.0000 0.9998 0.0000 0.1559 0.1032 1.0000 0.0233 1.0000 1.0000 0.0017 0.9999 0.5887 1.0000 1.0000
[67] 0.0244 0.0000 0.0000 0.9664 0.0005 0.0000 0.0166 1.0000 0.0106 1.0000 0.0000 0.9998 1.0000 0.9994

$combined
combined p-values with:      Stouffer's method
number of p-values combined: 79 
test statistic:              -Inf ~ N(0,1) 
adjustment:                  none 
combined p-value:            1 

Model 3: Full

FInally, the third model looks at everything (i.e. both physio and mood). This has an error rate of 43% which still sucks. Lets test this next against the bootstrap error #### Model {-}

# Then with the full model
vars.forest.x <-  c("mood_positive_c", "mood_negative_c",  "sc_tonic_mean", "sc_phasic_mag", "sc_phasic_dur", "sc_phasic_auc", "sc_phasic_num","hr_mean", "hr_max", "hr_min", "hr_sd", "acc_delta", "temp_mean")
forest.loso.full <- rf.loso(Data=EMA_Data, 
                       SubNr="castor_record_id", 
                       xvars=vars.forest.x,
                       yvar="Week_Type",
                       NoTree=5000)
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as.data.frame(forest.loso.full$error_rate)
psych::describe(forest.loso.full$error_rate*100)

Test

Finally we test the model with both against the null distribution.This one is also not significantly better than chance.

forest.loso_full_null <- rf.null_test(forest.loso.full, forest.boot.combi.merge, model_type="LOSO", method="actual")
forest.loso_full_null
$p_val
 [1] 0.0496 0.2528 0.0000 0.0485 0.0641 0.7740 0.0409 0.0000 0.0001     NA 0.0545 0.6610 0.6780 0.0003 1.0000 0.0000 0.0000 0.5450 0.5457 0.9957 0.0000 0.0000
[23] 0.0000 0.0000 0.0000 0.5653 0.8627 0.3768 0.0000 0.0000 0.0000 1.0000 0.0000 0.1334 0.0000 0.0000 0.0000 0.2496 0.0000 0.0000 0.0000 0.0000 0.0000 0.0062
[45] 0.0000 0.0000 0.0000 0.8257 0.0000 0.0000 0.3471 0.0000 0.0009 0.9658 0.0000 0.0002 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0002 0.0000 1.0000
[67] 0.0001 0.0001 0.0000 0.0000 0.0000 0.0629 0.0199 0.0000 1.0000 0.0155 0.0081 0.0000 0.6212 0.0078

$combined
combined p-values with:      Stouffer's method
number of p-values combined: 79 
test statistic:              -Inf ~ N(0,1) 
adjustment:                  none 
combined p-value:            1 

Based on all three tests for the models against the null we can conclude that the LOSO models do not in fact perform better than chance.

Whats the best LOSO?

Based on the error rate, lets see if one model does a better job than the other:

rf.loso.mood <- as.data.frame(forest.loso.mood$error_rate)
rf.loso.mood$id <- rownames(rf.loso.mood)
rf.loso.physio <- as.data.frame(forest.loso.physio$error_rate)
rf.loso.physio$id <- rownames(rf.loso.physio)
rf.loso.full <- as.data.frame(forest.loso.full$error_rate)
rf.loso.full$id <- rownames(rf.loso.full)
rf.result.merge <- merge(rf.loso.mood, rf.loso.physio, by="id")
rf.result.merge <- merge(rf.result.merge, rf.loso.full, by="id")
tidy(t.test(x=rf.result.merge$`forest.loso.mood$error_rate`, y=rf.result.merge$`forest.loso.physio$error_rate`, paired=T))
tidy(t.test(x=rf.result.merge$`forest.loso.mood$error_rate`, y=rf.result.merge$`forest.loso.full$error_rate`, paired=T))
tidy(t.test(x=rf.result.merge$`forest.loso.physio$error_rate`, y=rf.result.merge$`forest.loso.full$error_rate`, paired=T))

It looks like there is no significant difference between the error rates in the paired sample t-test in these three models. What could this mean? That regardless of what model we use at a population level, we still are not able to make decent predictions. I think that these models arent good at population level predictions, and this is pretty obnvious if we look at the within-subject variance from our linear models. Most of the variance comes from between subjects. Another approach is warranted.

5.4 Plot of Models

I next waht to make a plot of my models with the standard error. I first merge them into one dataframe, then I can actually plot them.

# I will rename the bootstrap coloumns so I can add them to the full model dataframe for plotting
df_boot1 <- forest.boot.mood.merge[,c("DataFrame.id" ,"averageError")]
df_boot1 <- df_boot1 %>% dplyr::rename(id=DataFrame.id, error=averageError) 
df_boot1 <- tibble::add_column(df_boot1, model="boot.mood", .after="id")
df_boot2 <- forest.boot.physio.merge %>% dplyr::select(DataFrame.id, averageError) %>% dplyr::rename(id=DataFrame.id, error=averageError) 
df_boot2 <- tibble::add_column(df_boot2, model="boot.physio", .after="id")
df_boot3 <- forest.boot.combi.merge %>% dplyr::select(DataFrame.id, averageError) %>% dplyr::rename(id=DataFrame.id, error=averageError) 
df_boot3 <- tibble::add_column(df_boot3, model="boot.full", .after="id")
# Join the boot straps
df_boot <- full_join(df_boot1, df_boot2) 
Joining, by = c("id", "model", "error")
df_boot <- full_join(df_boot, df_boot3)
Joining, by = c("id", "model", "error")
# Make the results and merge boot
df_loo <- gather(rf.combined.errors,model, error, loso.mood:lobo.full, factor_key=TRUE)
df_loo <- full_join(df_loo, df_boot)
Joining, by = c("id", "model", "error")
Column `model` joining factor and character vector, coercing into character vector
# Separate coloumns for plotting
df_loo <- separate(df_loo, model, into=c("Method", "Model"))
df_loo_sum <- data_summary(df_loo, "error", c("Method", "Model"))
# Set the SD and SE of bootstrap models to the correct ones of whole model
df_loo_sum$sd[df_loo_sum$Method=="boot" & df_loo_sum$Model=="mood"] <- boot.mood.descr$sd
df_loo_sum$se[df_loo_sum$Method=="boot" & df_loo_sum$Model=="mood"] <- boot.mood.descr$se
df_loo_sum$sd[df_loo_sum$Method=="boot" & df_loo_sum$Model=="physio"] <- boot.physio.descr$sd
df_loo_sum$se[df_loo_sum$Method=="boot" & df_loo_sum$Model=="physio"] <- boot.physio.descr$se
df_loo_sum$sd[df_loo_sum$Method=="boot" & df_loo_sum$Model=="full"] <- boot.combi.descr$sd
df_loo_sum$se[df_loo_sum$Method=="boot" & df_loo_sum$Model=="full"] <- boot.combi.descr$se
# Set the factor to make it pretty
df_loo_sum$Method <- factor(df_loo_sum$Method, levels =c("lobo", "loso", "boot"), labels = c("LOBO", "LOSO", "Bootstrap"))
df_loo_sum$Model<- factor(df_loo_sum$Model, levels =c("mood", "physio", "full"), labels = c("Model 1:\nMood", "Model 2:\n Physiology", "Model 3:\nCombination"))
figure.loo <- ggplot(df_loo_sum, aes(x=Model, y=error, colour=Method, fill=Method)) +
    geom_bar(stat="summary", position = position_dodge2()) + 
    geom_errorbar(aes(ymin=error-se, ymax=error+se), width=.2, position=position_dodge(.9), colour="black")  + 
    scale_y_continuous(breaks=c(0,10,20,30,40,50, 60, 70, 80), minor_breaks=c(5,15,25,35,45,55,65,75, 85) )+ 
    scale_colour_brewer(palette="Set2") + scale_fill_brewer(palette="Set2") + 
    xlab("")+ ylab("Error Rate (%)\n") + 
    theme(text=element_text(size=16,  family="Calibri"), 
          axis.line = element_line(size = 1, colour = "grey"),
          panel.background = element_rect(fill="transparent"),
        panel.grid.minor.y = element_line(colour="grey95"),
        panel.grid.major.y = element_line(colour = "grey95")); 
ggsave("figures/fig_RFModels.tiff", units="in", width=6, height=4, dpi=300, compression = 'lzw')
TIFFOpen: figures/fig_RFModels.tiff: No such file or directory.
figure.loo

5.5 Testing All Models

Now I want to see for each of the models, which one performs best. I first need to split the long dataframe I made for the figures into a wide format.

df_loo_wide <- pivot_wider(df_loo,id_cols = id, names_from=c(Method, Model), values_from=error)
print(df_loo_wide)

5.5.1 Model 1: Mood

LOBO vs Boot

tidy(t.test(df_loo_wide$lobo_mood, df_loo_wide$boot_mood , paired = T))

LOSO vs Boot

tidy(t.test(df_loo_wide$loso_mood, df_loo_wide$boot_mood , paired = T))

LOBO vs LOSO

tidy(t.test(df_loo_wide$lobo_mood, df_loo_wide$loso_mood , paired = T))

5.5.2 Model 2: Physio

LOBO vs Boot

tidy(t.test(df_loo_wide$lobo_physio, df_loo_wide$boot_physio , paired = T))

LOSO vs Boot

tidy(t.test(df_loo_wide$loso_physio, df_loo_wide$boot_physio , paired = T))

LOBO vs LOSO

tidy(t.test(df_loo_wide$lobo_physio, df_loo_wide$loso_physio , paired = T))

5.5.3 Model 3: Full Model

LOBO vs Boot

tidy(t.test(df_loo_wide$lobo_full, df_loo_wide$boot_full , paired = T))

LOSO vs Boot

tidy(t.test(df_loo_wide$loso_full, df_loo_wide$boot_full , paired = T))

LOBO vs LOSO

tidy(t.test(df_loo_wide$lobo_full, df_loo_wide$loso_full , paired = T))
---
title: "Predicting Ecologically Relevant Stress Exposure from Ambulatory Measures"
author: "Rayyan Tutunji"
output:
  html_notebook:
    number_sections: yes
    theme: flatly
    toc: yes
    toc_float: 
        collapsed: true 
  html_document:
    fig_height: 6
    fig_width: 9
    number_sections: yes
    theme: flatly
    toc: yes
    toc_depth: 4
    toc_float:
      collapsed: no
  pdf_document:
    toc: yes
  word_document:
    toc: yes
editor_options:
  chunk_output_type: inline
---


# Introduction


This is the notebook associated with the publication "TITLE". The code required to replicate the results can be found below. An additional accompanying file is also made avaiable in the same github directory containing the various functions used in this study. In a nutshell, participants unerwent 2 weeks of EMA, coupled with EPA (physiological arousal measures acquired via a wearable). One week has a high stakes exam, while the other is a control week. We look at the differences between the weeks, and then try to see momentary associations, followed by the ability of ML Models to classify the week types. Data can be made avaialbe upon request. Before we begin though, we load in all the libraries used. All libraries used must first be loaded. It may be that some libraries are not used, and that is due to edits and rewrites, but we keep them loaded just in case. 

```{r Import Libraries, echo=FALSE, message=FALSE, warning=FALSE, setup=TRUE}

#Cleaning Libs
library(readxl)
library (tidyverse)
library(plyr)
library(broom)
library (hablar)
library(janitor)
library(data.table)
library(zoo)
library(scales) # Rescaling made easy

# Library for EMA
library (remotes)
#remotes::install_github("wviechtb/esmpack") # commented, needs to be installed from github
library(esmpack)
library(boot) 

# Basic Stats
library (psych)
library (psycho)
library(Hmisc)
library(RcmdrMisc)
library(corrr)
library(ppcor)

# Mixed Model 
library (lmerTest)
library(optimx) # Optimizer for lm 
library(olsrr) # Diagnostic for lmer
library(sjPlot) # more modeling display
library(effectsize) # Get effect sizes from tstat
library(r2glmm) # Compute effect size directly
library(performance)
    

# Parallel processing
library(future)
library(doSNOW)
library(randomForest)

#Plotting
library(ggplot2) # Standard plotting
library(qgraph) # MLVAR Network Plotting
library(ggpubr)
library(knitr)

#PCA
library(factoextra)

#Fonts and Pretty things
library(stargazer)
library(extrafont)

#font_import()
loadfonts(device="pdf")
```

In addition to loading librarires, we also make a preset theme for the graphs to plot editing a bit easier. For that reason, we specify themes here. Additionally, we specify the number of cores we need, as this is important in perfroming some parallel analysis.
```{r}
# Theme 1
ggtheme <- theme (text=element_text(size=16,  family="Cambria"),
                  legend.position = "none",
                  axis.text.y = element_blank(),axis.text.x = element_text(size=16),
                  axis.ticks.y = element_blank(),
                  plot.title = element_text(size=16, hjust=0.5),
                  panel.background = element_rect(fill="transparent"),
                  panel.grid.minor.y = element_line(size=3),
                  panel.grid.major = element_line(colour = "aliceblue") )
# Theme 2
ptheme <- theme(text=element_text(size=11,  family="Calibri"), 
          axis.line = element_line(size = 1, colour = "grey"),
          panel.background = element_rect(fill="transparent"),
    plot.background = element_rect(fill = "transparent", color = NA), # bg of the plot
        panel.grid.minor.y = element_line(colour="grey95"),
        panel.grid.major.y = element_line(colour = "grey95")) 
  
# Set number of cores
NoCores <- as.numeric(availableCores())-1
  
```

Some custom functions were used as part of this study, and must be loaded. These functions are also provided in this github directory. 
```{r}
source("functions.R")
```

# Data

Now that all the set-up has been complete, we can start with loading the data. Due to privacy issues, only a specific file (and not the full file) with anonymized categorical variables for the program are provided in this code. This contains the same data used in the analysis, but with recoding of factors to mask potential identifiers. This has also been cleaned to generate a few different variables required for analysis using functions in the "function.R" file. These variables are given a specific suffix as described below: 

- _c: Variable is subject mean centered
- _z: Variable is z-transformed at the population level (centered and scaled)
- _s: Variable is Z-transformed and rescaled to 1-10 for analysis with different model families
- _m: Variable mean in each week for each subject 
- _mz: Variable mean from above is z-transformed
- _l: Variable is Temporally Lagged (-1)
- _cs: Variable is subject centered, then rescaled to 1-10

```{r}
#EMA_Data <- read.csv("data/EMA_Clean_Anon.csv")
print(EMA_Pub)
```

## Mean Stress

For some basic analysis, we also get the mean of the subjective stress measures. These are used for visualization. 
```{r}
# ##Average stress Measure
# EMA_Data$mean_stress <- rowSums(EMA_Data[c('event_tot_z', 'activity_tot_z', 'social_tot_z')], na.rm=TRUE)
# EMA_Data$mean_stress_c <- rowSums(EMA_Data[c('event_tot_c', 'activity_tot_c', 'social_tot_c')], na.rm=TRUE)
# EMA_Data$mean_stress_s <- scales::rescale(EMA_Data$mean_stress_c, to=c(1, 10))
# EMA_Data$mean_stress_l <- lag_var(x="mean_stress_c", id="Sub_nr_week", obs="obs", day= "ema_day_num", data=EMA_Data, lag=1)
# 
# ##Make Part into a factor variable for early and late
# EMA_Data$week_type <- EMA_Data$week_type-1
# EMA_Data$Week_Type <- factor(EMA_Data$week_type, levels=c('0','1'),
#                          labels=c('Control','Stress'))

```


# Descriptives Stats

Before running any stats, we should take a look at some descriptive stats to get an overall feel of our data.

## Compliance Rates  {.tabset}

Lets first check compliance rates to see how well our subjects adhered to the sampling. We first check the compliance rates uncorrected for the time at which they were acquired, followed by correction of the time limits. We set this to 1 hour since we only have 6 surveys, and our subjects had varying time schedules. It is indeed a limitation, but we had to do this for methodological reasons.

### Uncorrected Compliance {-}

Compliance rates uncorrected for time off-sets
```{r EMA Data: Check compliance}
# Recod compliance variable
EMA_Data$completed[EMA_Data$survey_progress==100] <- 1 
# Per subject
calc.nomiss(completed, castor_record_id, data=EMA_Data, prop=T)
# more summary statistics for compliance
summary(calc.nomiss(completed, castor_record_id, data=EMA_Data, prop=TRUE))

```

Without correcting for time offsets, our EMA measures seem to be nice. Lets see if I correct for timing if it makes a difference next what will happen. We will give participant one hour to finish the survey. If they dont finish it in that time window, we will count it as missing.

### Corrected Compliance {-}
Compliance rates correcting for time of completion.  first drop any survey that is not complete more than 80%. I then create a variabe that tells as when the survey was completed in terms of time (not date). I then conditionally set the completion variable to zero if the survey does not fall within the completed time window given the beep. 
```{r EMA Data: Check Compliance while account for Time}

# Set up some stuff for replace and refill
EMA_Data$survey_completed_on <- as.character(EMA_Data$survey_completed_on)
EMA_Data$survey_completed_time <- as.ITime(EMA_Data$survey_completed_on)
EMA_Data$completed[EMA_Data$survey_progress < 80] <- 0 

# Replace and refill conditionals for completion, factoring times
EMA_Data$completed[EMA_Data$survey_completed_time >= (as.ITime("10:30:00")) & EMA_Data$ema_beep==1] <- 0
EMA_Data$completed[EMA_Data$survey_completed_time >= (as.ITime("13:00:00")) & EMA_Data$ema_beep==2] <- 0
EMA_Data$completed[EMA_Data$survey_completed_time >= (as.ITime("15:30:00")) & EMA_Data$ema_beep==3] <- 0
EMA_Data$completed[EMA_Data$survey_completed_time >= (as.ITime("18:00:00")) & EMA_Data$ema_beep==4] <- 0
EMA_Data$completed[EMA_Data$survey_completed_time >= (as.ITime("20:30:00")) & EMA_Data$ema_beep==5] <- 0
EMA_Data$completed[EMA_Data$survey_completed_time >= (as.ITime("23:00:00")) & EMA_Data$ema_beep==6] <- 0

# Reformat 0 to Nan, and get new completion rates
EMA_Data$completed[EMA_Data$completed == 0] <- NA
calc.nomiss(completed, castor_record_id, data=EMA_Data,prop=TRUE)
summary(calc.nomiss(completed, castor_record_id, data=EMA_Data,prop=TRUE))

```

When we correct for the timing, we actually still have decent completion rates.

## Populations Descriptives {.tabset}

For the population descriptives, we use a different dataframe. So we oresent them below:

### Sex {-}
```{r}
describe(EMA_descr$Sex)
```
### Contraceptive Use {-}
```{r}
describe(factor(EMA_descr$Contraceptive_use))
```
### Program {-}
```{r}
describe((EMA_descr$Program))
```
### First Week {-}
```{r}
describe(EMA_descr$First_Week)
```
### Days Between Weeks {-}
```{r}
# Number of days between weeks
summary(abs(EMA_descr$Column1))
```
### Survey Disruption {-}
```{r}
psych::describe(EMA_Data$physical_disruption)
```


## Physiology Descriptives {.tabset}


After getting the population descriptives, we should next derive some E4 Quality measures. A lot of the data which is poor quality is already removed early on in the preprocessing pipeline. Instead we can check how many recordings were captured for the IBI data, and the overall movement during testing. 

### IBI Based Quality {-}
This is a measure of the total duration of IBI's detected in our windows. 
```{r}
ggplot(EMA_Data, aes(x=ibi_based_quality, colour=ibi_based_quality)) + geom_histogram()
count(EMA_Data$ibi_based_quality > 0.3)
mean(EMA_Data$ibi_based_quality, na.rm=T)

```

### IBI and ACC {-}
Next we will check if the IBI quality is related to the ACC data. This gives us a good idea of how much motion is affecting our data. 
```{r}
ggplot(EMA_Data, aes(x=ibi_based_quality, y=acc_delta)) + geom_smooth(method="lm", fullrange=F ) + coord_cartesian(ylim = c(0,10), xlim=c(0, 2.5))  + ggtheme + theme(axis.ticks.y=element_line(size=1), axis.text.y = element_text(size=12)) + ylab("ACC Delta") + xlab ("IBI Based Quality")

```

### IBI Quality and HR SD {-}
```{r}
ggplot(EMA_Data, aes(x=ibi_based_quality, y=hr_sd)) + geom_smooth(method="lm", fullrange=F ) + ggtheme + theme(axis.ticks.y=element_line(size=1), axis.text.y = element_text(size=12)) + ylab("HR SD") + xlab ("IBI Based Quality")
summary(lm(ibi_based_quality ~ hr_sd, data=EMA_Data))
```

### SC and ACC {-}
Next we will check if the SC signals are related to the ACC. Basically this is just doing explorartory analysis to double check certain things we already expect in our data. 
```{r}


fig.sc_tonic <- ggplot(EMA_Data, aes(x=sc_tonic_mean, y=acc_delta)) + geom_smooth(method="lm", fullrange=F )   + ggtheme + theme(axis.ticks.y=element_line(size=1), axis.text.y = element_text(size=12)) + ylab("ACC Delta") + xlab ("SC Tonic")  
fig.sc_mag <- ggplot(EMA_Data, aes(x=sc_phasic_mag, y=acc_delta)) + geom_smooth(method="lm", fullrange=F )   + ggtheme + theme(axis.ticks.y=element_line(size=1)) + xlab ("SC Mag") 

fig.sc_num <- ggplot(EMA_Data, aes(x=sc_phasic_num, y=acc_delta)) + geom_smooth(method="lm", fullrange=F )   + ggtheme + theme(axis.ticks.y=element_line(size=1)) + xlab ("SC Num") 

fig.sc_auc <- ggplot(EMA_Data, aes(x=sc_phasic_auc, y=acc_delta)) + geom_smooth(method="lm", fullrange=F )   + ggtheme + theme(axis.ticks.y=element_line(size=1)) +  xlab ("SC AUC") 

fig.sc_dur <- ggplot(EMA_Data, aes(x=sc_phasic_dur, y=acc_delta)) + geom_smooth(method="lm", fullrange=F )   + ggtheme + theme(axis.ticks.y=element_line(size=1)) + xlab ("SC Dur")  

fig.temp_mean <- ggplot(EMA_Data, aes(x=physical_excercise_dur, y=acc_delta, colour="red")) + geom_smooth(method="lm") + ggtheme 
ggarrange(fig.sc_tonic, fig.sc_mag, fig.sc_num, fig.sc_auc, fig.sc_dur, fig.temp_mean)

```

## Trends in EMA
I am curuious to see if there are trends in the EMA items too. Below I will plot the aggreagte data as a function of beep (EMA instance), separated by week.
```{r}

vars.ema <- c("mood_positive_z", "mood_negative_z", "event_tot_z", "activity_tot_z", "social_tot_z", "physical_tot_z")

plot.ema_trend <- list()
for ( i in vars.ema) {
    plot <- ggplot(EMA_Data, aes(y=get(i), x=ema_survey, colour=Week_Type)) + geom_line(stat="summary", aes(colour=Week_Type)) + geom_ribbon(aes(fill=Week_Type), stat="summary", alpha=0.3, colour=NA)+scale_x_continuous() + ylab(i)
    plot.ema_trend[[i]] <- plot
}
ggarrange(plotlist=plot.ema_trend, common.legend = T)

```

It looks like we have a bit of a trend in our data. The closer we are to the exams, the more stressed people become. We will need to add this to our models to correct for the trend statistically.


## Aggregate Stress {.tabset}

After plotting our variables over all the week, it will be interesting to check the aggregate stress changes, and how each subjects stress reactivity looks like. For this, I will make an average dataframe across the week, so we can look at the average change in mood. 

```{r Plot: Aggregate and Stress Change, warning=FALSE}

 
#Average Stress per Week:
EMA_avg <- EMA_Data
# Now I can do some merging
EMA_avg <- aggregate(EMA_avg, by=list(EMA_avg$castor_record_id, EMA_avg$Week_Type), FUN=mean, na.rm=T, na.warn=F)
EMA_avg$castor_record_id <- EMA_avg$Group.1
EMA_avg$Week_Type <- EMA_avg$Group.2
EMA_avg$Week_Type <- factor(EMA_avg$Week_Type, levels=c('Control','Stress'),
                     labels=c('Control','Exam'))

# Split the averaged DF to control and stress week
EMA_avg_exam <- subset(EMA_avg, Week_Type=="Exam") 
EMA_avg_control <- subset(EMA_avg, Week_Type!="Exam") 

# Merge by week to calculate change
EMA_avg_wide <-  merge(EMA_avg_exam, EMA_avg_control, by='castor_record_id', suffixes=c('_exam', '_control'))

# Make Aggregated variables 
EMA_avg_wide$mood_positive <-((EMA_avg_wide$mood_positive_control + EMA_avg_wide$mood_positive_exam)/2)
EMA_avg_wide$mood_negative <-((EMA_avg_wide$mood_negative_control + EMA_avg_wide$mood_negative_exam)/2)
EMA_avg_wide$activity_tot <-((EMA_avg_wide$activity_tot_control + EMA_avg_wide$activity_tot_exam)/2)
EMA_avg_wide$social_tot <-((EMA_avg_wide$social_tot_control + EMA_avg_wide$social_tot_exam)/2)
EMA_avg_wide$event_tot <-((EMA_avg_wide$event_tot_control + EMA_avg_wide$event_tot_exam)/2)
EMA_avg_wide$physical_tot <-((EMA_avg_wide$physical_tot_control + EMA_avg_wide$physical_tot_exam)/2)

# Make stress change, and mean centrer it
EMA_avg_wide$stress_reactivity <- EMA_avg_wide$mean_stress_exam - EMA_avg_wide$mean_stress_control
EMA_avg_wide$stress_reactivity_c <- EMA_avg_wide$mean_stress_c_exam - EMA_avg_wide$mean_stress_c_control
EMA_avg_wide$stress_reactivity_z <- scale(EMA_avg_wide$stress_reactivity, center = TRUE, scale = TRUE)

```


### Mean Change in Stress {-}
```{r}
#Box Plot
mean_box <- ggplot(EMA_avg, aes(y=mean_stress, x=Week_Type, colour=Week_Type,fill=Week_Type, na.rm = TRUE)) +
  geom_boxplot(alpha=1/2) + geom_jitter(width=0.1, alpha=1/2)+
  scale_y_continuous()+ scale_x_discrete()+
  ggtitle("Stress Levels per Week")+
  xlab("") + ylab("Aggregated stress measure\n")+ ggtheme
mean_box + coord_fixed(ratio=1.5)
```

### Stress Rectivity Heat Plot {-}
```{r}
scat_str <- ggplot (EMA_avg_wide, aes(y=stress_reactivity_c, x=factor(1), colour=stress_reactivity_c) ) +
    geom_jitter( width = 0.25, alpha=0.75, size = 2) +
    ggtitle("Individual Stress Reactivity to Exams\n")+ylab("Stress Reactivity\n")+labs(color = "Stress Reactivity\n")+
    theme(text=element_text(size=18,  family="Cambria"),
        plot.title=element_text (size=20, hjust=0.5),
        axis.title.x=element_blank(),axis.text.x=element_blank(),axis.ticks.x=element_blank(),
        axis.text.y = element_text(size=18),axis.title.y=element_text(size=18),
        panel.background = element_rect(fill="white"),
        panel.grid.minor.y = element_line(size=3),
        panel.grid.major = element_line(colour = "aliceblue"))
  scat_str + scale_color_gradient(low="blue", high="red") + coord_fixed(ratio = 0.6)
```
 
  
# Inferential Stats

Now we can do some statistical modeling with inferential stats. We use different glmer models for our data. The method used it simple: We fit the model multiple times with different families of models and different links. Based on the AIC, and the residuals, we pick the best fitting model. Additionally, we use a maximal fit approach. For our main fixed effect of interest, I also model a random slope and ranom intercept. For other covariates, I model them as fixed effects with random slopes and a fixed intercept. Subject is used as a random effect in all our models.   


## Week vs Week Differences

First we test our paradigm, and see whether it also has effects on our outcome measures of mood and physiological arousal. We check for main effects of week type (control or stress) on the variables. We also model covariates: Sex, Program, activity levels, and survey instance 

### Subjective Stress {.tabset }

Here we test the confirmatory analysis. We expect to see increased subjective stress in the stress week, which is confirmed in the models. For simplicity, we only present the final model selected based on the optimal fit.


#### Event Related Stress {-}
```{r}
# Model
glmer.event_week <- glmer(event_tot_s ~ Week_Type +  #Model week
    Sex + Program +  # Model sex and program 
    First_Week + ema_day*ema_beep_f + # Model day related items
    acc_delta +  physical_excercise_dur + acc_delta*physical_excercise_dur + # Model movement
    (1+Week_Type|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (0+ema_survey|castor_record_id) + (0+physical_excercise_dur|castor_record_id) + 
    (1|castor_record_id:ema_day:ema_beep_f),
    data=EMA_Data,
    family=gaussian,
    control=lmerControl(calc.derivs = FALSE))
# Model Summary
summary(glmer.event_week)

```


#### Activity Related Stress {-}
```{r}
# Model
glmer.activity_week <- glmer(activity_tot_s ~ Week_Type +  #Model week
    Sex + Program +  # Model sex and program 
    First_Week + ema_day*ema_beep_f + # Model day related items
    acc_delta +  physical_excercise_dur + acc_delta*physical_excercise_dur + # Model movement
    (1+Week_Type|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (0+ema_survey|castor_record_id) + (0+physical_excercise_dur|castor_record_id) + 
    (1|castor_record_id:ema_day:ema_beep_f),
    data=EMA_Data,
    family=gaussian,
    control=lmerControl(calc.derivs = FALSE))
# Model Summary
summary(glmer.activity_week )

```



#### Social Stress {-}
```{r}
# Model
glmer.social_week <- glmer( social_tot_s ~ Week_Type +  #Model week
    Sex + Program +  # Model sex and program 
    First_Week + ema_day*ema_beep_f + # Model day related items
    acc_delta +  physical_excercise_dur + acc_delta*physical_excercise_dur + # Model movement
    (1+Week_Type|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (0+ema_survey|castor_record_id) + (0+physical_excercise_dur|castor_record_id) + 
    (1|castor_record_id:ema_day:ema_beep_f),
    data=EMA_Data,
    family=Gamma(link="log"),
    control=glmerControl(calc.derivs = FALSE))
# Model Summary
summary(glmer.social_week)

```


#### Physical Stress {-}
```{r warning=FALSE}
# Model
glmer.physical_week<- glmer( physical_tot_s ~ Week_Type +  #Model week
    Sex + Program +  # Model sex and program 
    First_Week + ema_day*ema_beep_f + # Model day related items
    acc_delta +  physical_excercise_dur + acc_delta*physical_excercise_dur + # Model movement
    (1+Week_Type|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (0+ema_survey|castor_record_id) + (0+physical_excercise_dur|castor_record_id) + 
    (1|castor_record_id:ema_day:ema_beep_f),
    data=EMA_Data,
    #family=Gamma,
    control=lmerControl(calc.derivs = FALSE))
# Model Summary
summary(glmer.physical_week)

```  

#### Table and Plot{-}

To make things readable, we present the results in a simpler table. Additionally, we also present a plot for visualization. This is the same plot that is presented in our paper as figure 2. 
```{r}
tab_model(glmer.event_week, glmer.activity_week,  glmer.social_week, glmer.physical_week, 
           terms=c("(Intercept)","Week_Type [Stress]", "Sex [Male]", "Program [BSc_Med]", "First_Week [Exam-First]", "acc_delta", "physical_excercise_dur"), 
          dv.labels=c("Event", "Activity", "Social", "Physical"), 
          title="Table 1. Subjective Stress vs Week Type", show.df=T, show.fstat = T,
          transform=NULL, 
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
```

In the plot, we can see an increase in subjective stress measures for both event and activity realted stress during the exam week.

```{r}
# Subset the variables we want to plot
plot.mood_week <- plot_models(glmer.event_week, glmer.activity_week, glmer.social_week, glmer.physical_week)
rm_term <- as.vector(plot.mood_week$data$term[1:length(plot.mood_week$data$term)])
rm_term <- rm_term[rm_term != "Week_TypeStress"]

# Make the plot
plot.mood_week <- plot_models(glmer.event_week, glmer.activity_week, glmer.social_week, glmer.physical_week,
                                  m.labels=c("Event Stress", "Activity Stress","Social Stress", "Physical Stress" ),
                                  axis.labels = c(" "),
                                # Stastistical Stuff
                                rm.terms = rm_term,
                                show.p=T,
                                p.shape=T,
                                legend.pval.title = "Significance", 
                                # Visual Stuff
                                colors="#666666",
                                dot.size=2,
                                line.size = 1,
                                spacing=1 , 
                                vline.color = "darkgrey", 
                                legend.title = "") + ylab("\nParameter Estimate (a.u.)") + xlab("Subjective Stress") + 
                                ptheme + 
                                theme(axis.ticks.y=element_blank(), 
                                      legend.text=element_text(size=16), legend.title = element_text(size=16),
                                      axis.title = element_text(size=16),axis.text.x=element_text(size=11),
                                      panel.grid.major.x = element_line(colour = "grey95"),
                                      panel.grid.minor.x = element_line(colour = "grey90")) 

# Show and save
plot.mood_week+ coord_flip(ylim=c(-0.65,0.65)) + theme(panel.grid.major.y = element_line(colour = "grey95"), panel.grid.minor.y = element_line(colour = "grey90"))
#ggsave("figures/fig_WeekResid_SubjectiveStress.tiff",units="in", width=4, height=4, dpi=300, compression = 'lzw', bg="transparent")
```


### Mood {.tabset}

Next, we want to look at the mood outcome measures for positive and negative mood. I used the same covariates as before, and the same approach to modeling. That is, I fit all possible families and links, and picked the best fit.  

#### Positive Affect{-}
```{r warning=FALSE}
# Model
glmer.posmood_week <- glmer( mood_positive_s ~ Week_Type +  #Model week
    Sex + Program +  # Model sex and program 
    First_Week + ema_day*ema_beep_f + # Model day related items
    physical_excercise_dur + acc_delta + acc_delta*physical_excercise_dur + # Model movement
    (1+Week_Type|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (0+ema_survey|castor_record_id) + (0+physical_excercise_dur|castor_record_id) + 
    (1|castor_record_id:ema_day:ema_beep_f),
    data=EMA_Data,
    family=gaussian(link="log"),
    control=lmerControl(calc.derivs = FALSE))
# Model Summary
summary(glmer.posmood_week)

```

####  Negative Affect{-}
```{r warning=FALSE}
# Model
glmer.negmood_week <- glmer( mood_negative_s ~  Week_Type +  #Model week
    Sex + Program +  # Model sex and program 
    First_Week + ema_day*ema_beep_f + # Model day related items
    physical_excercise_dur + acc_delta + acc_delta*physical_excercise_dur + # Model movement
    (1+Week_Type|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (0+ema_survey|castor_record_id) + (0+physical_excercise_dur|castor_record_id) + 
    (1|castor_record_id:ema_day:ema_beep_f),
    data=EMA_Data,
    family=Gamma(link="log"),
    control=glmerControl(calc.derivs = FALSE))
# Model Summary
summary(glmer.negmood_week) 

```

#### Table {-}
Next we present the table of the results. We present a plot later that shows the results for all the outcomes, but for now we simply print the results of the mixed models
```{r}
tab_model(glmer.posmood_week, glmer.negmood_week,
          terms=c("(Intercept)","Week_Type [Stress]", "Sex [Male]", "Program [BSc_Med]", "First_Week [Exam-First]", "acc_delta", "physical_excercise_dur"), 
          dv.labels=c("Positive", "Negative"), 
          title="Table 2. Mood vs Week Type", 
          transform=NULL, 
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
```



### Phyisiology Stress

We also want to see if theres a general difference between the physiology variables and the weeks.To do this we build separate models for each physiology data feature. We also model the same covariates from before, but we also add to them temperature related changes, as we expect these to be highly singificant and related to our physiology. We present the results for the skin conductance and heart rate separately, and then together with FDR correction. 

#### Skin Conductance {.tabset .tabset-fade}

First we model the skin conductance, controlling for skin temparature. It looks like there is a big difference between the weeks, though not in the expected direction. For each model, we sekected the best family and link fit and present those below. 

##### Tonic SC {-} 
```{r warning=TRUE}
# Model
glmer.sc_ton_mean_week <- glmer( sc_tonic_mean_s ~ Week_Type + 
    Sex + Program + # Model pop differences
    First_Week +  ema_beep_f*ema_day + # Model day related differencxes
    physical_excercise_dur + acc_delta + # Modle movement stuff
    temp_mean_z + temp_slope_z +  # Model temp effects
    (1+Week_Type |castor_record_id) + 
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id) + 
    (0+physical_excercise_dur|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (1 | castor_record_id:ema_day:ema_beep_f), 
    EMA_Pub, 
    family=Gamma(link="log"),
    control=lmerControl(calc.derivs = FALSE) )
# Model Summary
summary(glmer.sc_ton_mean_week)
```


##### Phasic Num {-}
```{r warning=FALSE}
# Model
glmer.sc_ph_num <- glmer( sc_phasic_num ~  Week_Type + 
    Sex + Program + # Model pop differences
    First_Week +  ema_beep_f*ema_day + # Model day related differencxes
    physical_excercise_dur + acc_delta + # Modle movement stuff
    temp_mean_z + temp_slope_z +  # Model temp effects
    (1+Week_Type |castor_record_id) + 
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id) + 
    (0+physical_excercise_dur|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (1 | castor_record_id:ema_day:ema_beep_f),  
    EMA_Data, 
    family=poisson(link="log"),
    control=lmerControl(calc.derivs = FALSE) )
# Model Summary
summary(glmer.sc_ph_num)

```


##### Phasic Magnitude {-}
```{r warning=FALSE}
# Model
glmer.sc_ph_mag <- glmer( sc_phasic_mag_s ~ Week_Type + 
    Sex + Program + # Model pop differences
    First_Week +  ema_beep_f*ema_day + # Model day related differencxes
    physical_excercise_dur +acc_delta + # Modle movement stuff
    temp_mean_z + temp_slope_z +  # Model temp effects
    (1+Week_Type |castor_record_id) + 
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id) + 
    (0+physical_excercise_dur|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (1 | castor_record_id:ema_day:ema_beep_f), 
    EMA_Data, 
    family=Gamma(link="identity"),
    control=lmerControl(calc.derivs = FALSE) )
# Model Summary
summary(glmer.sc_ph_mag)

```


##### Phasic AUC {-}
```{r}
# Model
glmer.sc_ph_auc_week <- glmer( sc_phasic_auc_s  ~ Week_Type + 
    Sex + Program + # Model pop differences
    First_Week +  ema_beep_f*ema_day + # Model day related differencxes
    physical_excercise_dur +acc_delta + # Modle movement stuff
    temp_mean_z + temp_slope_z +  # Model temp effects
    (1+Week_Type |castor_record_id) + 
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id) + 
    (0+physical_excercise_dur|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (1 | castor_record_id:ema_day:ema_beep_f), 
    EMA_Data, 
    family=Gamma(link=log),
    control=lmerControl(calc.derivs = FALSE) )
# Model Summary
summary(glmer.sc_ph_auc_week)

``` 


##### Table{-}
Hear we can see that overall the measures seem to go down. We still need to correct for multiple comparrisons, but we can do this at the end when we also factor in our heart rate models to also include that informaiton in the FDR correction.
```{r}
tab_model(glmer.sc_ton_mean_week, glmer.sc_ph_num, glmer.sc_ph_mag, glmer.sc_ph_auc_week, 
         terms=c("(Intercept)","Week_Type [Stress]", "Sex [Male]", "Program [BSc_Med]", "First_Week [Exam-First]", "acc_delta", "physical_excercise_dur"), 
          dv.labels=c("Tonic", "Number", "Magnitude", "AUC"), 
          title="Table 3. SC vs Week Type", 
          transform=NULL, 
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
```


#### Heart Rate {.tabset}

We now take a look at the heart rate models. As the IBI data was way too sparse, it would be difficult to analyze the temporal domain changes. So we stick to simple measures of heart rate from the E4. Again, we fit the different families and links, and present the optimal fits below. 

##### HR Mean {-}
```{r}
# Model
glmer.hr_mean_week <- glmer( hr_mean_s ~ Week_Type + 
    Sex + Program + # Model pop differences
    First_Week +  ema_beep_f*ema_day + # Model day related differencxes
    physical_excercise_dur +acc_delta + # Modle movement stuff
    temp_mean_z + temp_slope_z +  # Model temp effects
    (1+Week_Type |castor_record_id) + 
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id) + 
    (0+physical_excercise_dur|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (1 | castor_record_id:ema_day:ema_beep_f), 
    EMA_Data, 
    family=Gamma(link=identity),
    control=lmerControl(calc.derivs = FALSE) )
# Model Summary
summary(glmer.hr_mean_week)

```


##### HR Max {-}
```{r}
# Model
glmer.hr_max_week <- glmer( hr_max_s  ~ Week_Type + 
    Sex + Program + # Model pop differences
    First_Week +  ema_beep_f*ema_day + # Model day related differencxes
    physical_excercise_dur +acc_delta + # Modle movement stuff
    temp_mean_z + temp_slope_z +  # Model temp effects
    (1+Week_Type |castor_record_id) + 
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id) + 
    (0+physical_excercise_dur|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (1 | castor_record_id:ema_day:ema_beep_f),  
    EMA_Data, 
    family=Gamma(link="identity"),
    control=lmerControl(calc.derivs = FALSE) )
# Model SUmmary
summary(glmer.hr_max_week)

```


##### HR Min {-}
```{r}
# Model
glmer.hr_min_week <- glmer( hr_min_s  ~ Week_Type + 
    Sex + Program + # Model pop differences
    First_Week +  ema_beep_f*ema_day + # Model day related differencxes
    physical_excercise_dur +acc_delta + # Modle movement stuff
    temp_mean_z + temp_slope_z +  # Model temp effects
    (1+Week_Type |castor_record_id) + 
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id) + 
    (0+physical_excercise_dur|castor_record_id) + (0+acc_delta|castor_record_id) + 
    (1 | castor_record_id:ema_day:ema_beep_f), 
    EMA_Data, 
    family=Gamma(link="identity"),
    control=lmerControl(calc.derivs = FALSE) )
# Model Summary
summary(glmer.hr_min_week)

```



##### Table {-}

```{r}
tab_model(glmer.hr_mean_week, glmer.hr_min_week, glmer.hr_max_week, glmer.hr_sd_week, 
          terms=c("(Intercept)","Week_Type [Stress]", "Sex [Male]", "Program [BSc_Med]", "First_Week [Exam-First]", "acc_delta", "physical_excercise_dur"), 
          dv.labels=c("Mean", "Min", "Max", "SD"), 
          title="Table 3. HR vs Week Type", #p.adjust = "fdr",
          transform=NULL, 
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
```

#### Table and Plot: Physiology vs Weektype

I will now make a table for all physiology measures.These tables will also have the FDR adjusted values that we report in our article. 
```{r}
tab_model(glmer.sc_ton_mean_week, glmer.sc_ph_num, glmer.sc_ph_mag, glmer.sc_ph_auc_week, glmer.hr_mean_week, glmer.hr_min_week, glmer.hr_max_week, 
         terms=c("(Intercept)","Week_Type [Stress]", "Sex [Male]", "Program [BSc_Med]", "First_Week [Exam-First]", "acc_delta", "physical_excercise_dur", 
         "temp_mean_z", "temp_slope_z"), 
          dv.labels=c("SC Tonic", "SC Number", "SC Magnitude", "SC AUC", "HR Mean", "HR Min", "HR Max"), 
          title="Table 3. Physio vs Week Type", 
          transform=NULL, p.adjust="fdr",
         show.stat=TRUE,
         show.se=T) %>%  
    return() %$%
    knitr %>%
    asis_output()
```

### Plot: Outcome Measures
And now I also plot the figure we use in the article with all the outcome measures including the affect items. I again do FDR correction here.
```{r}
# Together
plot.physio <- plot_models(glmer.posmood_week, glmer.sc_ton_mean_week, glmer.sc_ph_num)
rm_term <- as.vector(plot.physio$data$term[1:97])
rm_term <- rm_term[rm_term != "Week_TypeStress"]
# Color list
col_list <-c('#7570B3','#7570B3','#7570B3',"#D95F02", "#D95F02", '#D95F02', '#D95F02', "#1B9E77", "#1B9E77")

# Make the plot
plot.all_week_resid <- plot_models( glmer.posmood_week, glmer.negmood_week, 
            glmer.sc_ton_mean_week, glmer.sc_ph_num, glmer.sc_ph_mag, glmer.sc_ph_auc_week, 
            glmer.hr_mean_week, glmer.hr_min_week, glmer.hr_max_week,
            m.labels=c("Positive Affect", "Negative Affect", "SC Tonic", "SC Number", "SC Magnitued", "SC AUC","HR Mean", "HR Minimum", "HR Maximum"),
            axis.labels = c(" "),
            # Stastistical Stuff
            rm.terms = rm_term,
            #show.values = T,
            #value.size = 4, 
            #std.est=T, 
            show.p=T,
            p.shape=T,
            p.adjust = "fdr", 
            legend.pval.title = "Significance", 
            # Visual Stuff
            colors=col_list,
            dot.size=2,
            line.size = 1,
            spacing=0.7, 
            vline.color = "darkgrey", 
            legend.title = "") + 
            ptheme + 
            theme(axis.ticks.y=element_blank(), 
                  legend.text=element_text(size=16), legend.title = element_text(size=16),
                  axis.title = element_text(size=16),axis.text.x=element_text(size=11),
                  panel.grid.major.x = element_line(colour = "grey95"),
                  panel.grid.minor.x = element_line(colour = "grey90")) 

# Plot and save
plot.all_week_resid + coord_flip(ylim=c(-0.5,0.5)) + theme(panel.grid.major.y = element_line(colour = "grey95"), panel.grid.minor.y = element_line(colour = "grey90"))
#ggsave("figures/fig_WeekResid_ALL.tiff", units="in", width=4, height=4, dpi=300, compression = 'lzw', bg="transparent")
```

## {.unlisted .unnumbered}

So overall all, our first analysis confirms that our stress week results in increased stress. This has a direct consequence on mood outcomes, and physiology. But the physiology is not really in the expected direction which is a bit strange. Interestingly though, the physiology is in the same direction as positive affect. So this indicated to me maybe that we are looking at reductions in positive arousal.


## Momentary Associations

Now we found week differences in both the EMA and EPA measures, the next step will be to investigate the relaitonship between subjective stress as and our outcome measures on a beep to beep level. This is a bit of a replicaiton attempt of previous studies, where we also try to explain the previous findings. Is it linked to positive affect as well?

For these models, we know that activity stress is correlated with event and social stress, which we present below. So to adjust for that, we also model interaction terms for these variables specifically. We model similar covariates, but not day here, only time of day since we arent looking at the weeks in a linear fashion. Due to convergence issues with the maximal models, we have a fixed intercept for our fixed effects of interest in these models. 

### Correlation Matrix{-} 
```{r}
 rcorr(as.matrix(EMA_Data[,c("event_tot_s", "activity_tot_s", "social_tot_s", "physical_tot_s")]))
```


### Mood {.tabset}

First we take a look at the affect/mood items.We use the maximal fitting with all the families and links, and pick the best fit for our results.

#### Positive {-}
```{r}

glmer.posmood_beep <- glmer(mood_positive_s ~ 
    event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=gaussian(link="identity"),
    control=lmerControl(calc.derivs = FALSE) )
# Summary
summary(glmer.posmood_beep )
```

#### Negative {-}
```{r}
glmer.negmood_beep <- glmer(mood_negative_s ~ 
    event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="identity"),
    control=glmerControl(calc.derivs = FALSE) )

# Summary
summary(glmer.negmood_beep)
```

#### Table: Mood{-}

Now I can present a table of nelow to make it a little prettier. 
```{r}
tab_model(glmer.posmood_beep, glmer.negmood_beep,
         # terms=c("(Intercept)","Week_Type [Stress]", "Sex [Male]", "Program [BSc_Med]", "First_Week [Exam-First]", "acc_delta", "physical_excercise_dur"), 
          title="Table 3. HR vs Week Type", 
          transform=NULL, p.adjust = "fdr",
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
```



### Skin conductance {.tabset}

Next we will also chekc the skin conductance measures for the moment-to-moment effects. Perhaps in the weeks the physiology measures arent increased, but in moments of stress they are. We again fit the models with different families and links, and pick the best fit which is presented here.

#### Tonic Mean {-}
```{r}
# Model
glmer.sc_ton_ema <- glmer(sc_tonic_mean_s ~ 
    event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="log"),
    control=glmerControl(calc.derivs = FALSE) )

# Summary
summary(glmer.sc_ton_ema)
```


#### Phasic Number {-}
```{r}
# Model
glmer.sc_ph_num_ema <- glmer(sc_phasic_num  ~ 
    event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=poisson(link="sqrt"),
    control=lmerControl(calc.derivs = FALSE) )

# Model Summary
summary(glmer.sc_ph_num_ema)
```


#### Phasic Magnitude {-}
```{r}
# Model
glmer.sc_ph_mag_ema <- glmer(sc_phasic_mag_s   ~
    event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="identity"),
    control=lmerControl(calc.derivs = FALSE) )

# Model Summary
summary(glmer.sc_ph_mag_ema)
```


#### Phasic AUC {-}
```{r}
# Model
glmer.sc_ph_auc_ema <- glmer(sc_phasic_auc_s  ~
     event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="identity"),
    control=lmerControl(calc.derivs = FALSE) )

# Model Summary
summary(glmer.sc_ph_auc_ema)
```


#### Table: Skin Conductance {-}
Now I make a table for the SC measures. I do not use FDR here, as I only do this in the finaly table we present in the artcle
```{r}
tab_model(glmer.sc_ton_ema, glmer.sc_ph_num_ema, glmer.sc_ph_mag_ema, glmer.sc_ph_auc_ema,
         # terms=c("(Intercept)","Week_Type [Stress]", "Sex [Male]", "Program [BSc_Med]", "First_Week [Exam-First]", "acc_delta", "physical_excercise_dur"), 
          title="Table X. SC v Subjective Stress", 
          transform=NULL,
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
```



### Heart Rate{.tabset}

Finally we can check the heart rate and moment to moment subjective stress. Same goes as before (families and links tests, only optimal shown).

#### Mean {-}
```{r}
# Model
glmer.hr_mean_ema <- glmer(hr_mean_s ~
    event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="identity"),
    control=glmerControl(calc.derivs = FALSE) )

# Model Summary
summary(glmer.hr_mean_ema)
```


#### Min {-}
```{r}
# Model
glmer.hr_min_ema <- glmer(hr_min_s  ~
    event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="log"),
    control=lmerControl(calc.derivs = FALSE) )

# Model Summary
summary(glmer.hr_min_ema)
```


#### Max {-}
```{r}
# Model
glmer.hr_max_ema <- glmer(hr_max_s ~
    event_tot_s*activity_tot_s + activity_tot_s*social_tot_s + physical_tot_s +
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex +  physical_excercise_dur + acc_delta +
    temp_mean_z + temp_slope_z + 
    (0+event_tot_s+activity_tot_s+social_tot_s+physical_tot_s | castor_record_id) + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="identity"),
    control=lmerControl(calc.derivs = FALSE) )

# Model Summary
summary(glmer.hr_max_ema)

```


#### Table: Heart Rate{-}
We now make a table for the heart rate measures for easier visualization. 
```{r}
tab_model(glmer.hr_mean_ema, glmer.hr_min_ema, glmer.hr_max_ema, 
          dv.labels=c("Mean", "Min", "Max"), 
          title="Table X. Heart rate vs. Subjective Stress",
            transform=NULL, 
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
```


### Table: Physiology v Subjective Stress
We now build the table for all the physiology measures, and apply the FDR correction to these models. These are the statistics we report in the article. 
```{r}
tab_model(glmer.sc_ton_ema, glmer.sc_ph_num_ema, glmer.sc_ph_mag_ema, glmer.sc_ph_auc_ema, 
            glmer.hr_mean_ema, glmer.hr_min_ema, glmer.hr_max_ema, 
          dv.labels=c("SC Tonic", "SC Number", "SC Magnitude", "SC AUC", "HR Mean", "HR Min", "HR Max"), 
          title="Table X. Momentary Physiology and Subjective Stress",
            transform=NULL, p.adjust="fdr", 
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
```



### Plot: Outcomes v Subjective Stress


Next we plot our outcomes as a function of the subjective stress. We build four graphs, one for each of the subjective stress types. These graphs are presented in the results section of the article (figure 3).
```{r}
# Shorrtlist the variables to those of interest
plot.vars <- plot_models(glmer.posmood_beep, glmer.sc_ph_num_ema, glmer.hr_mean_ema, glmer.hr_min_ema, glmer.hr_max_ema)
# Get and filter terms
full_term <- as.vector(plot.vars$data$term[1:length(plot.vars$data$term)])
event_term <- full_term[full_term != "event_tot_s"]
activ_term <-full_term[full_term != "activity_tot_s"]
soc_term <- full_term[full_term != "social_tot_s"]
phy_term <- full_term[full_term != "physical_tot_s"]
# Set the colours
col_list <-c('#7570B3','#7570B3','#7570B3',"#D95F02", "#D95F02", '#D95F02', '#D95F02', "#1B9E77", "#1B9E77")

# Event Plot
plot.event_substr <- plot_models(glmer.posmood_beep, glmer.negmood_beep, 
            glmer.sc_ton_ema, glmer.sc_ph_num_ema, glmer.sc_ph_mag_ema, glmer.sc_ph_auc_ema, 
            glmer.hr_mean_ema, glmer.hr_min_ema, glmer.hr_max_ema, 
            m.labels=c("Positive Affect", "Negative Affect", "SC Tonic", "SC Number", "SC Magnitued", "SC AUC", "HR Mean", "HR Minimum", "HR Maximum"),
            axis.labels = c(""), 
            # Stastistical Stuff
            rm.terms = event_term,
            #show.values = T,
            #value.size = 4, 
            #std.est=T, 
            show.p=T,
            p.shape=T,
            p.adjust = "fdr", 
            legend.pval.title = "Significance", 
            # Visual Stuff
            colors=col_list,
            dot.size=2,
            line.size = 0.5,
            spacing=0.7, 
            vline.color = "darkgrey", 
            legend.title = "") + 
            ptheme + 
            theme(axis.ticks.y=element_blank(), 
                  axis.title = element_text(size=16),axis.text.x=element_text(size=11),
                  panel.grid.major.x = element_line(colour = "grey95"),
                  panel.grid.minor.x = element_line(colour = "grey90")) 
plot.event_substr <- plot.event_substr+ coord_flip(ylim=c(0.75,1.25)) +  coord_flip(ylim=c(-0.5,0.5)) + theme(panel.grid.major.y = element_blank(), panel.grid.minor.y = element_blank())
#ggsave("figures/fig_StrResid_Event.tiff", units="in", width=4, height=4, dpi=300, compression = 'lzw', bg="transparent")

# Act Plot
plot.activity_substr <-  plot_models(glmer.posmood_beep, glmer.negmood_beep, 
            glmer.sc_ton_ema, glmer.sc_ph_num_ema, glmer.sc_ph_mag_ema, glmer.sc_ph_auc_ema, 
            glmer.hr_mean_ema, glmer.hr_min_ema, glmer.hr_max_ema, 
            m.labels=c("Positive Affect", "Negative Affect", "SC Tonic", "SC Number", "SC Magnitued", "SC AUC", "HR Mean", "HR Minimum", "HR Maximum"),
            axis.labels = c(""), 
            # Stastistical Stuff
            rm.terms = activ_term,
            #show.values = T,
            #value.size = 4, 
            #std.est=T, 
            show.p=T,
            p.shape=T,
            p.adjust = "fdr", 
            legend.pval.title = "Significance", 
            # Visual Stuff
            colors=col_list,
            dot.size=2,
            line.size = 0.5,
            spacing=0.7, 
            vline.color = "darkgrey", 
            legend.title = "") + 
            ptheme + 
              theme(axis.ticks.y=element_blank(), 
                  axis.title = element_text(size=16),axis.text.x=element_text(size=11),
                  panel.grid.major.x = element_line(colour = "grey95"),
                  panel.grid.minor.x = element_line(colour = "grey90")) 
plot.activity_substr <- plot.activity_substr+ coord_flip(ylim=c(0.75,1.25)) +  coord_flip(ylim=c(-0.5,0.5)) + theme(panel.grid.major.y = element_blank(), panel.grid.minor.y = element_blank())
#ggsave("figures/fig_StrResid_Activity.tiff", units="in", width=4, height=4, dpi=300, compression = 'lzw', bg="transparent")


# Social Stress
plot.social_substr <-  plot_models(glmer.posmood_beep, glmer.negmood_beep, 
            glmer.sc_ton_ema, glmer.sc_ph_num_ema, glmer.sc_ph_mag_ema, glmer.sc_ph_auc_ema, 
            glmer.hr_mean_ema, glmer.hr_min_ema, glmer.hr_max_ema, 
            m.labels=c("Positive Affect", "Negative Affect", "SC Tonic", "SC Number", "SC Magnitued", "SC AUC", "HR Mean", "HR Minimum", "HR Maximum"),
            axis.labels = c(""), 
            # Stastistical Stuff
            rm.terms = soc_term,
            #show.values = T,
            #value.size = 4, 
            #std.est=T, 
            show.p=T,
            p.shape=T,
            p.adjust = "fdr", 
            legend.pval.title = "Significance", 
            # Visual Stuff
            colors=col_list,
            dot.size=2,
            line.size = 0.5,
            spacing=0.7, 
            vline.color = "darkgrey", 
            legend.title = "") + 
            ptheme + 
            theme(axis.ticks.y=element_blank(), 
                  axis.title = element_text(size=16),axis.text.x=element_text(size=11),
                  panel.grid.major.x = element_line(colour = "grey95"),
                  panel.grid.minor.x = element_line(colour = "grey90")) 
## Plot
plot.social_substr <- plot.social_substr + coord_flip(ylim=c(0.75,1.25)) +  coord_flip(ylim=c(-0.5,0.5)) + theme(panel.grid.major.y = element_blank(), panel.grid.minor.y = element_blank())
#ggsave("figures/fig_StrResid_Social.tiff", units="in", width=4, height=4, dpi=300, compression = 'lzw', bg="transparent")

# Physical Stress
plot.physical_substr <- plot_models(glmer.posmood_beep, glmer.negmood_beep, 
            glmer.sc_ton_ema, glmer.sc_ph_num_ema, glmer.sc_ph_mag_ema, glmer.sc_ph_auc_ema, 
            glmer.hr_mean_ema, glmer.hr_min_ema, glmer.hr_max_ema, 
            m.labels=c("Positive Affect", "Negative Affect", "SC Tonic", "SC Number", "SC Magnitued", "SC AUC", "HR Mean", "HR Minimum", "HR Maximum"),
            axis.labels = c(""), 
            # Stastistical Stuff
            rm.terms = phy_term,
            #show.values = T,
            #value.size = 4, 
            #std.est=T, 
            show.p=T,
            p.shape=T,
            p.adjust = "fdr", 
            legend.pval.title = "Significance", 
            # Visual Stuff
            colors=col_list,
            dot.size=2,
            line.size =0.5,
            spacing=0.7, 
            vline.color = "darkgrey", 
            legend.title = "") + 
            ptheme + 
              theme(axis.ticks.y=element_blank(), 
                  axis.title = element_text(size=16),axis.text.x=element_text(size=11),
                  panel.grid.major.x = element_line(colour = "grey95"),
                  panel.grid.minor.x = element_line(colour = "grey90")) 
# Plot
plot.physical_substr <- plot.physical_substr +  coord_flip(ylim=c(-0.5,0.5), xlim=c(1,1.1)) + theme(panel.grid.major.y = element_blank(), panel.grid.minor.y = element_blank())
#ggsave("figures/fig_StrResid_Physical.tiff", units="in", width=4, height=4, dpi=300, compression = 'lzw', bg="transparent")

# All
ggarrange(plot.event_substr, plot.activity_substr, plot.social_substr, plot.physical_substr, common.legend = T, legend="right")
#ggsave("figures/fig_StrResid_MAT.tiff", units="in", width=7, height=7, dpi=300, compression = 'lzw', bg="transparent")
```

# {.unlisted .unnumbered}

So we only see event related and physical stress have a relationship with SC magnitude. Thats cools, and somewhat replicates some previous findings from Smets et al. 2018. 

## Mood and Physio

Since we think this is an arousal related mechanism, we would also need to establish the link to physiology. To this end, we check the relationship between physiology and the mood items. We see a high correlation between positive and negative mood (presented below). So we also model interaction terms here. Due to model convergence issues, we only model the fixed intercepts here for the fixe effects of interest. Again, we check all model families before we pick the one with the best fit. 

### Skin Conductance {.tabset}

#### Tonic Mean {-}
```{r}
# Model
glmer.sc_ton_mood <- glmer(sc_tonic_mean_s ~ mood_positive_s*mood_negative_s + 
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex + temp_slope_z + temp_mean_z + 
    acc_delta + physical_excercise_dur +
    (0+mood_positive_s*mood_negative_s| castor_record_id) +# + (1+mood_negative_s|castor_record_id)+
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="log"),
    control=glmerControl(calc.derivs = FALSE) )

# Summary
summary(glmer.sc_ton_mood)
```

#### Phasic Number {-}
```{r}
# Model
glmer.sc_phnum_mood <- glmer(sc_phasic_num_s ~ mood_positive_s*mood_negative_s + 
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex + temp_slope_z + temp_mean_z + 
    acc_delta + physical_excercise_dur +
    (0+mood_positive_s*mood_negative_s| castor_record_id) +
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="identity"),
    control=glmerControl(calc.derivs = FALSE) )
# Summary
summary(glmer.sc_phnum_mood)
```

#### Phasic Magnitude {-}
```{r}
# Model
glmer.sc_ph_mag_mood <- glmer(sc_phasic_mag_s ~ mood_positive_s*mood_negative_s + 
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex + temp_slope_z + temp_mean_z + 
    acc_delta + physical_excercise_dur +
    (1+mood_positive_s*mood_negative_s| castor_record_id)  + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
  family=Gamma(link="identity"),
    control=glmerControl(calc.derivs = FALSE) )

# Summary
summary(glmer.sc_ph_mag_mood)
```


#### Phasic AUC {-}
```{r}
# Model
glmer.sc_ph_auc_mood <- glmer(sc_phasic_auc_s ~ mood_positive_s*mood_negative_s + 
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex + temp_slope_z + temp_mean_z + 
    acc_delta + physical_excercise_dur +
    (1+mood_positive_s*mood_negative_s| castor_record_id)  +
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="log"),
    control=glmerControl(calc.derivs = FALSE) )
# Summary
summary(glmer.sc_ph_auc_mood)
```

#### Table: Sc vs Mood {-}
Now we make a table, without the FDR correction. This we do later with the full modles in the table. 
```{r}
tab_model(glmer.sc_ton_mood, glmer.sc_phnum_mood, glmer.sc_ph_mag_mood, glmer.sc_ph_auc_mood, 
          dv.labels=c("Tonic", "Number", "Magnitude", "AUC"), 
          title="Table X. SCR and Mood",
            transform=NULL,
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
```


### Heart Rate {.tabset}

#### Mean {-}
```{r}

glmer.hr_mean_mood <- glmer(hr_mean_s ~ mood_positive_s*mood_negative_s + 
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex + temp_slope_z + temp_mean_z + 
    acc_delta + physical_excercise_dur +
    (1+mood_positive_s*mood_negative_s| castor_record_id)  + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="log"),
    control=glmerControl(calc.derivs = FALSE) )

# Summary
summary(glmer.hr_mean_mood)
```


#### Min {-}
```{r}
glmer.hr_min_mood <- glmer(hr_min_s ~ mood_positive_s*mood_negative_s + 
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex + temp_slope_z + temp_mean_z + 
    acc_delta + physical_excercise_dur +
    (1+mood_positive_s*mood_negative_s| castor_record_id)  + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="log"),
    control=glmerControl(calc.derivs = FALSE) )

# Summary
summary(glmer.hr_min_mood )
```

#### Max {-}
```{r}
glmer.hr_max_mood <- glmer(hr_max_s ~ mood_positive_s*mood_negative_s + 
    ema_beep + # I will model the beep to factor circadian rhythms
    Sex + temp_slope_z + temp_mean_z + 
    acc_delta + physical_excercise_dur +
    (1+mood_positive_s*mood_negative_s| castor_record_id)  + 
    (0+ema_beep|castor_record_id)+
    (0+temp_slope_z|castor_record_id) + (0+temp_mean_z|castor_record_id)+
    (0+acc_delta|castor_record_id) + (0+physical_excercise_dur|castor_record_id),
    EMA_Data,
    family=Gamma(link="log"),
    control=glmerControl(calc.derivs = FALSE) )

# Summary
summary(glmer.hr_max_mood )
```

#### Table: HR v Mood {-}
Again, we make a table of the heart rate measures without the FDR correction. We apply that later.
```{r}
tab_model(glmer.hr_mean_mood, glmer.hr_min_mood, glmer.hr_max_mood, 
          dv.labels=c("Mean", "Min", "Max"), 
          title="Table X. Heart rate vs. Mood",
            transform=NULL, 
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
```


### Table and Plot: Mood and Physiology

Now I can actually print the tables, and the plot along with the FDR  correction. 
```{r}
tab_model(glmer.sc_ton_mood, glmer.sc_phnum_mood, glmer.sc_ph_mag_mood, glmer.sc_ph_auc_mood,
                glmer.hr_mean_mood, glmer.hr_min_mood, glmer.hr_max_mood,
          dv.labels=c("SC Tonic", "SC Number", "SC Magnitude", "SC AUC", "HR Mean", "HR Min", "HR Max"), 
          title="Table X. Physio vs. Mood",
            transform=NULL, p.adjust="fdr", 
         show.stat=TRUE,
         show.se=TRUE) %>%  
    return() %$%
    knitr %>%
    asis_output()
```


```{r}
# Subset variables of interests
plot.physio <- plot_models(glmer.sc_ton_mood, glmer.sc_phnum_mood, glmer.hr_mean_mood)
rm_term <- as.vector(plot.physio$data$term[1:97])
rm_term <- rm_term[rm_term != "mood_positive_s" & rm_term!="mood_negative_s"]
# Set the colours
col_list <-c('#7570B3','#7570B3','#7570B3',"#D95F02", "#D95F02", '#D95F02', '#D95F02', "#1B9E77", "#1B9E77")


# Make the plot
plot.pos_mood_resid <- plot_models( glmer.sc_ton_mood, glmer.sc_phnum_mood, glmer.sc_ph_mag_mood, glmer.sc_ph_auc_mood,
                glmer.hr_mean_mood, glmer.hr_min_mood, glmer.hr_max_mood,
              m.labels=c("SC Tonic", "SC Number", "SC Magnitued", "SC AUC","HR Mean", "HR Minimum", "HR Maximum"),
           axis.labels = c(" "),
            # Stastistical Stuff
           transform=NULL,
            rm.terms = rm_term,
            #show.values = T,
            #value.size = 4, 
            #std.est=T, 
            show.p=T,
            p.shape=T,
            p.adjust = "fdr", 
            legend.pval.title = "Significance", 
            # Visual Stuff
            colors=col_list,
            dot.size=2,
            line.size = 1,
            spacing=0.7, 
            vline.color = "darkgrey", 
            legend.title = "") + 
            ptheme + scale_y_continuous(breaks=c( -0.2, -.1,0, .1,.2)) + 
            theme(axis.ticks.y=element_blank(), 
                  axis.title = element_text(size=16),axis.text.x=element_text(size=11),
                  panel.grid.major.x = element_line(colour = "grey95"),
                  panel.grid.minor.x = element_line(colour = "grey90")) 
# Plot and Save
plot.pos_mood_resid + coord_flip(ylim=c(-.25,.25)) + theme(panel.grid.major.y = element_line(colour = "grey95"), panel.grid.minor.y = element_line(colour = "grey90"))
#ggsave("figures/fig_MoodkResid_ALL.tiff", units="in", width=5, height=5, dpi=300, compression = 'lzw', bg="transparent")
```





## Mediation anaylsis

In the stress week, we see a decreease in both positive mood and physiology. However, we also see an increase in stress, which we know is related to some physiology (specifically, SC magnitude). So we need to actually confirm that what we see in the stress week (i.e. the physiology arousal decrease) is actually due to the positive mood changes. To this end, we perfrom a mediation analysis. We first need to filter out the nan's here for some reason though, and we cant really add any covariates in an easy way. So we will stick to the simplest model here. 

```{r}
library(mediation)
set.seed(123)

EMA_Sub <- EMA_Data %>% dplyr::select(castor_record_id, Week_Type, sc_phasic_mag_s, mood_positive_s, event_tot_s) %>% filter(complete.cases(.))
```


### Positive Mood

Now that we have filtered the data, we run the first of the mediation analyses. Here we test whether the effect of week on the SC measures is mediated by positive mood. 
```{r}
# Set up


# Main effect
fit.totaleffect=glmer(sc_phasic_mag_s ~ Week_Type  + (1|castor_record_id), EMA_Sub)
summary(fit.totaleffect)

# Mediations
fit.mediator=glmer(mood_positive_s ~ Week_Type  + (1|castor_record_id), EMA_Sub)
summary(fit.mediator)

# Combined
fit.dv=glmer(sc_phasic_mag_s ~ Week_Type + mood_positive_s  + (1|castor_record_id), EMA_Sub)
summary(fit.dv)

# Mediation analysis
results = mediate(model.m=fit.mediator, model.y=fit.dv, treat='Week_Type', mediator='mood_positive_s', boot=F, sims=5000)
summary(results)

```

The results show that indeed, the results are mediated by positive mood. 

### Event Stress
We now need to refit the models and check whether event stress is doing any supression or mediation. So we run another model to check that. 
```{r}

# Main effect
fit.totaleffect=glmer(sc_phasic_mag_s ~ Week_Type  + (1|castor_record_id), EMA_Sub)
summary(fit.totaleffect)

# Mediations
fit.mediator=glmer(event_tot_s ~ Week_Type  + (1|castor_record_id), EMA_Sub)
summary(fit.mediator)

# Combined
fit.dv=glmer(sc_phasic_mag_s ~ Week_Type + event_tot_s   + (1|castor_record_id), EMA_Sub)
summary(fit.dv)

# Mediation analysis
results2 = mediate(model.m=fit.mediator, model.y=fit.dv, treat='Week_Type', mediator='event_tot_s', boot=F, sims=5000)
summary(results2)

```
Here, we see that indeed there is no mediation 


# Random Forests

We were able to establish that physiology and mood both change in the weeks under chronic stress. That is good, because now we can see how well we can use this informaiton in predictive models. To this end, we use the randomForest package plus some extra functions to test our prediction. Firrst lets set a seed and load a packacge for these analyses. 
```{r}
library(randomForest)
set.seed(123)
```

## OOB Error {.tabset}
Before going into the details of the models, we first subset the data to omit any nans. We then check the out of back error for random forest models predicting week from the data types. We run three models predicting week type from each of the following:

1. Affect
2. Physiology
3. Combination

After checking the OOB errors, we can split the data into the training/testing sets.
```{r}
# Variables for Forest
vars.forest <- c( "Week_Type", "mood_positive", "mood_negative", "sc_tonic_mean", "sc_phasic_mag", "sc_phasic_dur", "sc_phasic_auc", "sc_phasic_num","hr_mean", "hr_max", "hr_min", "hr_sd", "acc_delta", "temp_mean")
vars.forest.physio <-c( "sc_tonic_mean", "sc_phasic_mag", "sc_phasic_dur", "sc_phasic_auc", "sc_phasic_num","hr_mean", "hr_max", "hr_min", "hr_sd", "Week_Type" )

# Subset the data
df.RandomForest <- EMA_Data[,vars.forest]
df.RandomForest <- na.omit(df.RandomForest)
df.RandomForest.physio <- df.RandomForest[,vars.forest.physio]
``` 

### Mood {-}
This modle classifies week type from the affect items
```{r}
# Run random forest model for mood vars
forest.mood <- randomForest(Week_Type ~ mood_positive + mood_negative,
                            data=df.RandomForest, 
                            ntree=5000,
                          importance = TRUE)
forest.mood
```

### Physio {-}
Now we can check what the physio data looks like. The OOB is 38.43 for the mood data. Can we do better with the full data? And what is the most important variable in these models?
```{r}
# Run random forest full model
vars.forest.physio <- c( "sc_tonic_mean", "sc_phasic_mag", "sc_phasic_dur", "sc_phasic_auc", "sc_phasic_num","hr_mean", "hr_max", "hr_min", "hr_sd", "acc_delta", "temp_mean")
forest.full <- randomForest( as.formula(paste("Week_Type", "~", (paste(vars.forest.physio, collapse="+")))) ,
                            data=df.RandomForest, 
                            ntree=5000,
                            importance = TRUE)
forest.full
randomForest::importance(forest.full)
```


### Full {-}

Next up I will select the all variables and see if it improves our model. 
```{r}
# Run the forest with most important features
forest.important <- randomForest(Week_Type ~ .,
                            data=df.RandomForest, 
                            ntree=5000,
                            importance = TRUE)
forest.important
```


Ok so first I looked at the random forest models as a whole without really doing any type of validation of the predictions. We can see that if we look at the mood, we get better predictions for stress and control weeks than looking at the whole set of physio parameters. Thats interesting, but unsurprising. We now need to do some testing and validation. 

## LOBO

In order to the validation, we try out a leave-one-beep-out (LOBO) analysis. This analysis will run a random forest model for each subject separately, leaving out one survey when running the model. We then test the model on the beep that was left out. We repeat this process for the subject until we've removed each survey/beep out once. This results in a series of predictions that give us an error level for each subject. In order to do this, we have developed a function that is provided in this github directory.

### Model 1: Mood {-}


#### Model {-}
We first run the LOBO model using the custom function.
```{r}
# Then with the full model
vars.forest.mood <-  c("mood_positive_c", "mood_negative_c")
forest.lobo.mood <- rf.lobo(Data=EMA_Data,
                              SubNr="castor_record_id",
                           xvars=vars.forest.mood,
                              yvar="Week_Type",
                              NoTree=5000)
as.data.frame(forest.lobo.mood$total$subject_errors)
psych::describe(forest.lobo.mood$total$subject_errors)

```



#### Bootstrap{-}
We see we get an estimated error of around 33% for this model. Thats cool. Now we need to test it against the random error. One can assume in theory that the prediction error for a dichotomous variable is 50/50, but we dont like to do things the easy way. Instead, we will do 10000 iterations where we bootstrap resample the stress and control weeks. This will give us the real error rate with a sampling distribution. This was made into a function, but for some reason I couldnt get the function to run in parallel. So instead I run the parallel processing of the bootstrap outside of a function. Its not pretty, but it works. 
```{r warning=FALSE}
# BootstrapLOBO.
# { cl <- makeCluster(NoCores-1)
# registerDoSNOW(cl)
# iterations <- 10000
# print("Running, this will take a while...", quote=F)
# pb <- txtProgressBar(max = iterations, style = 3)
# progress <- function(n) setTxtProgressBar(pb, n)
# opts <- list(progress = progress)
# forest.boot.mood <- foreach(i=1:iterations, .options.snow = opts ) %dopar% {
#     rf.BootstrapError(Data=EMA_Data,
#                           Shuffle="Week_Type",
#                           Iterations=1,
#                           SubjectId="castor_record_id",
#                           xvar=vars.forest.mood,
#                           yvar="Week_Type",
#                           Trees=500)
# }
# print("Done!", quote=F)
# stopCluster(cl)
# # Now merge them into one dataframe
# pb <- txtProgressBar(max =length(forest.boot.mood), style = 3)
# forest.boot.mood.merge <- as.data.frame(forest.boot.mood[[1]][2])
# for (i in 2:length(forest.boot.mood)) {
#     setTxtProgressBar(pb, i)
#     df.2merge <- as.data.frame(forest.boot.mood[[i]][2])
#     forest.boot.mood.merge <- merge (df.2merge, forest.boot.mood.merge , by="DataFrame.id")
# }
# # After merging the results into a single data frame, lets also everage the error rate
# forest.boot.mood.merge$averageError <- rowMeans(forest.boot.mood.merge [, -which(names( forest.boot.mood.merge) %in% c("DataFrame.id"))], na.rm=T)
# saveRDS(forest.boot.mood.merge, file = "data/bootstrap_mood.rds")
# }
``` 


Now that we have run the bootstrap, we also save it just in case, and then we get the average error, and calcualte the true SD and SE from the sampling distribution. 
```{r}
# Print the Errors
boot.mood.descr <- psych::describe(forest.boot.mood.merge$averageError)
# Also get the true SD of bootstraps
boot.mood.descr$sd <- mean((psych::describe(forest.boot.mood.merge))$sd, na.rm=T)
boot.mood.descr$se <- mean((psych::describe(forest.boot.mood.merge))$se, na.rm=T)
boot.mood.descr

```

 
#### Stouffer's Test{-}
I will now test the LOBO model using Mood against the bootstrapped LOBO model with the same variables. I made a function to do this. The finction will first calculate a z-score for each subject based on the distribution of the bootstrapped models, then it will calculate the P-value from the z-score. Finally the function sums the z-scores using the stouffer method. Using this method, we see the LOBO models perfrom significantly better than chance. Yay! So within-subject approach works super well! 

```{r}

lobo.mood_null <- rf.null_test(forest.lobo.mood, forest.boot.mood.merge, model_type="LOBO", method="actual")
lobo.mood_null
```




### Model 2: Physio {-}

The second model I will test is whether we can predict week type from the physiology data alone. For this, I run the model first to get the LOBO error rate.

#### Model {-}
We see that it does a bit worse than model 1. But we still need to check the bootstrap error for the model with the physio data. It should be similar to that of the mood though.
```{r}
# Then with the full model
vars.forest.physio <-  c("sc_tonic_mean", "sc_phasic_mag", "sc_phasic_dur", "sc_phasic_auc", "sc_phasic_num","hr_mean", "hr_max", "hr_min", "hr_sd", "acc_delta", "temp_mean")
forest.lobo.physio <- rf.lobo(Data=EMA_Data,
                              SubNr="castor_record_id",
                              xvars=vars.forest.physio,
                              yvar="Week_Type",
                              NoTree=5000)
as.data.frame(forest.lobo.physio$total$subject_errors)
psych::describe(forest.lobo.physio$total$subject_errors)

```

#### Bootstrap{-}
We again do the bootstrap model, and then save it as an object for later use. 
```{r}
# # LOBO Bootstrapping
# { cl <- makeCluster(NoCores-1)
#     registerDoSNOW(cl)
#     iterations <- 10000
#     print("Running, this will take a while...", quote=F)
#     pb <- txtProgressBar(max = iterations, style = 3)
#     progress <- function(n) setTxtProgressBar(pb, n)
#     opts <- list(progress = progress)
#     forest.boot.physio <- foreach(i=1:iterations, .options.snow = opts ) %dopar% {
#         rf.BootstrapError(Data=EMA_Data,
#                                           Shuffle="Week_Type",
#                                           Iterations=1,
#                                           SubjectId="castor_record_id",
#                                           xvar=vars.forest.physio,
#                                           yvar="Week_Type",
#                                           Trees=500)
#     }
#     print("Done!", quote=F)
#     stopCluster(cl)
#     
#     # Now merge them into one dataframe
#     pb <- txtProgressBar(max =length(forest.boot.physio), style = 3)
#     forest.boot.physio.merge <- as.data.frame(forest.boot.physio[[1]][2])
#     for (i in 2:length(forest.boot.physio)) {
#         setTxtProgressBar(pb, i)
#         df.2merge <- as.data.frame(forest.boot.physio[[i]][2])
#         forest.boot.physio.merge <- merge(df.2merge, forest.boot.physio.merge , by="DataFrame.id",
#                                           suffixes=c((paste(i,".x")),(paste(i,".y"))))
#     }
#     # Merge it to mean
#     forest.boot.physio.merge$averageError <- rowMeans(forest.boot.physio.merge [, -which(names( forest.boot.physio.merge) %in% c("DataFrame.id"))], na.rm=T)
#     saveRDS( forest.boot.physio.merge, file = "data/bootstrap_physio.rds")
# }
```

We now calculate the bootstrap SE and SD
```{r}
# Print the Errors
boot.physio.descr <- psych::describe(forest.boot.physio.merge$averageError)
# Also get the true SD of bootstraps
boot.physio.descr$sd <- mean((psych::describe(forest.boot.physio.merge))$sd, na.rm=T)
boot.physio.descr$se <- mean((psych::describe(forest.boot.physio.merge))$se, na.rm=T)
boot.physio.descr
```

#### Stouffer's Test{-}

So now that I have the averaged bootstrap error for the physio model, lets check if the LOBO is more than random with a test against the bootstrap estimates. 
```{r}
lobo.physio_null <- rf.null_test(forest.lobo.physio, forest.boot.physio.merge,  model_type="LOBO", method="actual")
lobo.physio_null

```

According to the t-test against the bootstrap error sample, the test is above chance level here too. I will again do a model comparison at the end of the model-testing sections.

### Model 3: Full {-}

Finally we check the full model using both physio and mood variables.

#### Model{-}
```{r}
# Then with the full model
vars.forest.x <-  c("mood_positive_c", "mood_negative_c", "sc_tonic_mean", "sc_phasic_mag", "sc_phasic_dur", "sc_phasic_auc", "sc_phasic_num","hr_mean", "hr_max", "hr_min", "hr_sd", "temp_mean")
forest.lobo.full <- rf.lobo(Data=EMA_Data,
                              SubNr="castor_record_id",
                              xvars=vars.forest.x,
                              yvar="Week_Type",
                              NoTree=5000)
as.data.frame(forest.lobo.full$total$subject_errors)
psych::describe(forest.lobo.full$total$subject_errors)

``` 


#### Bootstrap{-}
Then I can check the bootstrap error for the model combined model as done before:
```{r}
# {cl <- makeCluster(NoCores-1)
# registerDoSNOW(cl)
# iterations <- 10000
# print("Running, this will take a while...", quote=F)
# pb <- txtProgressBar(max = iterations, style = 3)
# progress <- function(n) setTxtProgressBar(pb, n)
# opts <- list(progress = progress)
# forest.boot.combi <- foreach(i=1:iterations, .options.snow = opts ) %dopar% {
#     rf.BootstrapError(Data=EMA_Data,
#                                       Shuffle="Week_Type",
#                                       Iterations=1,
#                                       SubjectId="castor_record_id",
#                                       xvar=vars.forest.x,
#                                       yvar="Week_Type",
#                                       Trees=500)
# }
# print("Done!", quote=F)
# stopCluster(cl)
# 
# # Now merge them into one dataframe
# pb <- txtProgressBar(max =length(forest.boot.combi), style = 3)
# forest.boot.combi.merge <- as.data.frame(forest.boot.physio[[1]][2])
# for (i in 2:length(forest.boot.combi)) {
#     setTxtProgressBar(pb, i)
#     df.2merge <- as.data.frame(forest.boot.combi[[i]][2])
#     forest.boot.combi.merge <- merge(df.2merge, forest.boot.combi.merge , by="DataFrame.id",
#                                       suffixes=c((paste(i,".x")),(paste(i,".y"))))
# }
# # Merge it to mean
# forest.boot.combi.merge$averageError <- rowMeans(forest.boot.combi.merge [, -which(names( forest.boot.combi.merge) %in% c("DataFrame.id"))], na.rm=T)
#  saveRDS( forest.boot.combi.merge, file = "data/bootstrap_combi.rds")
# }
```

We then again calculate the SE and SD of the models
```{r}
# Print the Errors
boot.combi.descr <- psych::describe(forest.boot.combi.merge$averageError)
# Also get the true SD of bootstraps
boot.combi.descr$sd <- mean((psych::describe(forest.boot.combi.merge))$sd, na.rm=T)
boot.combi.descr$se <- mean((psych::describe(forest.boot.combi.merge))$se, na.rm=T)
boot.combi.descr

```

#### Stouffer's Test{-}
And finally I can test the difference between the full model and the bootstrapped one. So we can see again, that our model only improves slightly with the addition of the physio variables (1%). That doesnt seem great. But we can also guess that within the control week there may be times when people are stressed, and vice versa for the stress week.We will do the null test again.

```{r}
lobo.combi_null <- rf.null_test(forest.lobo.full, forest.boot.combi.merge, model_type="LOBO", method="actual")
lobo.combi_null
```



### Whats the best LOBO? {-}

Now that we've established all our models do better than the bootstrap version, we can also test the models against each other. We first check the lowest performers. 

#### Mood vs Physio

We filter the data and have to do a couple of manipulations to do a paired t-test.We see that the mood does significantly better

```{r}

rf.result.df1 <- as.data.frame(forest.lobo.physio$total$subject_errors)
colnames(rf.result.df1)[1] <- "physio"
rf.result.df1$id <- rownames(rf.result.df1)

rf.result.df2 <- as.data.frame(forest.lobo.mood$total$subject_errors)
colnames(rf.result.df2)[1] <- "mood"
rf.result.df2$id <- rownames(rf.result.df2)

rf.result.merge <- merge(rf.result.df1, rf.result.df2, by="id")
tidy(t.test(x=rf.result.merge$physio, y=rf.result.merge$mood, paired=T))
```


#### Combi vs Mood

Now I test the mood vs full model. It appears that the full model does a lot better than the one with mood only. So it is safe to say that Model 3 > Model 1 > Model 2
```{r}

rf.result.df1 <- as.data.frame(forest.lobo.full$total$subject_errors)
colnames(rf.result.df1)[1] <- "full"
rf.result.df1$id <- rownames(rf.result.df1)

rf.result.df2 <- as.data.frame(forest.lobo.mood$total$subject_errors)
colnames(rf.result.df2)[1] <- "mood"
rf.result.df2$id <- rownames(rf.result.df2)

rf.result.merge <- merge(rf.result.df1, rf.result.df2, by="id")
tidy(t.test(x=rf.result.merge$full, y=rf.result.merge$mood, paired=T))
```




## LOSO

Next up is the standard LOSO. The idea here is that we want to check if we can actually use the data of different participants to predict for a completetly new one. This will remove the enitre EMA data set of a single subject, run the model, then cross validate it with the subject that was left out. I can now run the function below, first with a vector only including the mood items, then the full model:

### Model 1: Mood {-}

#### Model{-}
Our first model looks at the mood ratings predicting which week participants are in. I estimate the LOSO error rates below. The model here doesnt do as well as the model with the lobo. Lets try to use the LOBO null distribution to see if its above chance levels next.
```{r}
# First with mood items
vars.forest.mood <-  c("mood_positive", "mood_negative")
forest.loso.mood <- rf.loso(Data=EMA_Data, 
                       SubNr="castor_record_id", 
                       xvars=vars.forest.mood,
                       yvar="Week_Type",
                       NoTree=5000)
as.data.frame(forest.loso.mood$error_rate)
psych::describe(forest.loso.mood$error_rate*100, na.rm=T)

```

#### Test {-}
Here I will try to check the LOSO model vs. the null distribution estimated from the bootstrap we did earler. The loso model did not perform better than the bootstrapped estimates.
```{r}

forest.loso_mood_null <- rf.null_test(forest.loso.mood, forest.boot.mood.merge,  model_type="LOSO", method="actual")
forest.loso_mood_null

```


### Model 2: Physio {-}

The second model is looking at the physio variables predicting week type. We see that it only achieves 47.83% success. We will test this now against the bootstrapped error rate.
#### Model{-}
```{r}
# Then with the full model
vars.forest.physio <-  c("sc_tonic_mean", "sc_phasic_mag", "sc_phasic_dur", "sc_phasic_auc", "sc_phasic_num","hr_mean", "hr_max", "hr_min", "hr_sd", "acc_delta", "temp_mean")
forest.loso.physio <- rf.loso(Data=EMA_Data, 
                       SubNr="castor_record_id", 
                       xvars=vars.forest.physio,
                       yvar="Week_Type",
                       NoTree=5000)
as.data.frame(forest.loso.physio$error_rate)
psych::describe(forest.loso.physio$error_rate*100)
``` 

#### Test{-}
Next we check the physio variables against the null distribution. Here we see that it its also not signficantly better than chance.
```{r}
forest.loso_physio_null <- rf.null_test(forest.loso.physio, forest.boot.physio.merge, model_type="LOSO", method="actual")
forest.loso_physio_null
```

### Model 3: Full {-}
FInally, the third model looks at everything (i.e. both physio and mood). This has an error rate of 43% which still sucks. Lets test this next against the bootstrap error
#### Model {-}
```{r}
# Then with the full model
vars.forest.x <-  c("mood_positive_c", "mood_negative_c",  "sc_tonic_mean", "sc_phasic_mag", "sc_phasic_dur", "sc_phasic_auc", "sc_phasic_num","hr_mean", "hr_max", "hr_min", "hr_sd", "acc_delta", "temp_mean")
forest.loso.full <- rf.loso(Data=EMA_Data, 
                       SubNr="castor_record_id", 
                       xvars=vars.forest.x,
                       yvar="Week_Type",
                       NoTree=5000)
as.data.frame(forest.loso.full$error_rate)
psych::describe(forest.loso.full$error_rate*100)

``` 
#### Test {-}
Finally we test the model with both against the null distribution.This one is also not significantly better than chance.  
```{r}
forest.loso_full_null <- rf.null_test(forest.loso.full, forest.boot.combi.merge, model_type="LOSO", method="actual")
forest.loso_full_null

```

Based on all three tests for the models against the null we can conclude that the LOSO models do not in fact perform better than chance. 

### Whats the best LOSO? {-}

Based on the error rate, lets see if one model does a better job than the other:
```{r}
rf.loso.mood <- as.data.frame(forest.loso.mood$error_rate)
rf.loso.mood$id <- rownames(rf.loso.mood)

rf.loso.physio <- as.data.frame(forest.loso.physio$error_rate)
rf.loso.physio$id <- rownames(rf.loso.physio)

rf.loso.full <- as.data.frame(forest.loso.full$error_rate)
rf.loso.full$id <- rownames(rf.loso.full)

rf.result.merge <- merge(rf.loso.mood, rf.loso.physio, by="id")
rf.result.merge <- merge(rf.result.merge, rf.loso.full, by="id")

tidy(t.test(x=rf.result.merge$`forest.loso.mood$error_rate`, y=rf.result.merge$`forest.loso.physio$error_rate`, paired=T))
tidy(t.test(x=rf.result.merge$`forest.loso.mood$error_rate`, y=rf.result.merge$`forest.loso.full$error_rate`, paired=T))
tidy(t.test(x=rf.result.merge$`forest.loso.physio$error_rate`, y=rf.result.merge$`forest.loso.full$error_rate`, paired=T))
```

It looks like there is no significant difference between the error rates in the paired sample t-test in these three models. What could this mean? That regardless of what model we use at a population level, we still are not able to make decent predictions. I think that these models arent good at population level predictions, and this is pretty obnvious if we look at the within-subject variance from our linear models. Most of the variance comes from between subjects. Another approach is warranted.


## Plot of Models

I next waht to make a plot of my models with the standard error. I first merge them into one dataframe, then I can actually plot them. 
```{r}

# I will rename the bootstrap coloumns so I can add them to the full model dataframe for plotting
df_boot1 <- forest.boot.mood.merge[,c("DataFrame.id" ,"averageError")]
df_boot1 <- df_boot1 %>% dplyr::rename(id=DataFrame.id, error=averageError) 
df_boot1 <- tibble::add_column(df_boot1, model="boot.mood", .after="id")
df_boot2 <- forest.boot.physio.merge %>% dplyr::select(DataFrame.id, averageError) %>% dplyr::rename(id=DataFrame.id, error=averageError) 
df_boot2 <- tibble::add_column(df_boot2, model="boot.physio", .after="id")
df_boot3 <- forest.boot.combi.merge %>% dplyr::select(DataFrame.id, averageError) %>% dplyr::rename(id=DataFrame.id, error=averageError) 
df_boot3 <- tibble::add_column(df_boot3, model="boot.full", .after="id")
# Join the boot straps
df_boot <- full_join(df_boot1, df_boot2) 
df_boot <- full_join(df_boot, df_boot3)
# Make the results and merge boot
df_loo <- gather(rf.combined.errors,model, error, loso.mood:lobo.full, factor_key=TRUE)
df_loo <- full_join(df_loo, df_boot)
# Separate coloumns for plotting
df_loo <- separate(df_loo, model, into=c("Method", "Model"))



df_loo_sum <- data_summary(df_loo, "error", c("Method", "Model"))
# Set the SD and SE of bootstrap models to the correct ones of whole model
df_loo_sum$sd[df_loo_sum$Method=="boot" & df_loo_sum$Model=="mood"] <- boot.mood.descr$sd
df_loo_sum$se[df_loo_sum$Method=="boot" & df_loo_sum$Model=="mood"] <- boot.mood.descr$se
df_loo_sum$sd[df_loo_sum$Method=="boot" & df_loo_sum$Model=="physio"] <- boot.physio.descr$sd
df_loo_sum$se[df_loo_sum$Method=="boot" & df_loo_sum$Model=="physio"] <- boot.physio.descr$se
df_loo_sum$sd[df_loo_sum$Method=="boot" & df_loo_sum$Model=="full"] <- boot.combi.descr$sd
df_loo_sum$se[df_loo_sum$Method=="boot" & df_loo_sum$Model=="full"] <- boot.combi.descr$se

# Set the factor to make it pretty
df_loo_sum$Method <- factor(df_loo_sum$Method, levels =c("lobo", "loso", "boot"), labels = c("LOBO", "LOSO", "Bootstrap"))
df_loo_sum$Model<- factor(df_loo_sum$Model, levels =c("mood", "physio", "full"), labels = c("Model 1:\nMood", "Model 2:\n Physiology", "Model 3:\nCombination"))

figure.loo <- ggplot(df_loo_sum, aes(x=Model, y=error, colour=Method, fill=Method)) +
    geom_bar(stat="summary", position = position_dodge2()) + 
    geom_errorbar(aes(ymin=error-se, ymax=error+se), width=.2, position=position_dodge(.9), colour="black")  + 
    scale_y_continuous(breaks=c(0,10,20,30,40,50, 60, 70, 80), minor_breaks=c(5,15,25,35,45,55,65,75, 85) )+ 
    scale_colour_brewer(palette="Set2") + scale_fill_brewer(palette="Set2") + 
    xlab("")+ ylab("Error Rate (%)\n") + 
    theme(text=element_text(size=16,  family="Calibri"), 
          axis.line = element_line(size = 1, colour = "grey"),
          panel.background = element_rect(fill="transparent"),
        panel.grid.minor.y = element_line(colour="grey95"),
        panel.grid.major.y = element_line(colour = "grey95")); 
#ggsave("figures/fig_RFModels.tiff", units="in", width=4, height=4, dpi=300, compression = 'lzw')
figure.loo
```

## Testing All Models

Now I want to see for each of the models, which one performs best. I first need to split the long dataframe I made for the figures into a wide format.
```{r}
df_loo_wide <- pivot_wider(df_loo,id_cols = id, names_from=c(Method, Model), values_from=error)
print(df_loo_wide)
```


### Model 1: Mood {.tabset}

#### LOBO vs Boot {-}
```{r}
tidy(t.test(df_loo_wide$lobo_mood, df_loo_wide$boot_mood , paired = T))

```

#### LOSO vs Boot {-}

```{r}
tidy(t.test(df_loo_wide$loso_mood, df_loo_wide$boot_mood , paired = T))

```

#### LOBO  vs LOSO {-}
```{r}

tidy(t.test(df_loo_wide$lobo_mood, df_loo_wide$loso_mood , paired = T))
```


### Model 2: Physio {.tabset}

#### LOBO vs Boot {-}
```{r}

tidy(t.test(df_loo_wide$lobo_physio, df_loo_wide$boot_physio , paired = T))

```

#### LOSO vs Boot {-}

```{r}

tidy(t.test(df_loo_wide$loso_physio, df_loo_wide$boot_physio , paired = T))

```


#### LOBO  vs LOSO {-}
```{r}

tidy(t.test(df_loo_wide$lobo_physio, df_loo_wide$loso_physio , paired = T))

```



### Model 3: Full Model {.tabset}

#### LOBO vs Boot {-}
```{r}

tidy(t.test(df_loo_wide$lobo_full, df_loo_wide$boot_full , paired = T))

```

#### LOSO vs Boot {-}

```{r}

tidy(t.test(df_loo_wide$loso_full, df_loo_wide$boot_full , paired = T))

```


#### LOBO  vs LOSO {-}
```{r}

tidy(t.test(df_loo_wide$lobo_full, df_loo_wide$loso_full , paired = T))

```



